Experimental test of shrinking matter theory?

[PeterDonis]

OK - fair enough.

Imagine...

You need to stop waving your hands and "imagining" things and start actually doing math, using the equations given in Wetterich's paper, if you want to keep constructing scenarios. This is not a case where you can just use your intuitions, because the whole point of the model in the paper is that it violates the intuitions that underlie the standard model of cosmology.

 

[PeterDonis]

Moderator's note: Thread level changed to "A" since the proposed model under discussion requires that level of knowledge of the subject matter.

 

[PeterDonis]

Imagine...

As far as a response to my response is concerned, the shell and everything inside it is still a gravitationally bound system, whether "space is expanding" outside it or not, so both models--standard cosmology and Wetterich's model--predict the same observations for the shell and inside it.

 

[PeterDonis]

The only direct observable is convergence of particles with some initial state of motion.

Yes, and that direct observable is what increases without bound as the Big Bang singularity is approached in the standard cosmology model. (In the standard cosmology model, the Ricci scalar $R$ basically corresponds to this observable, but the fact remains that the physical prediction of the standard cosmology model is a prediction about the observable.) So it is impossible for Wetterich's model to "represent the same physics" in that regime if it has no singularity, since "no singularity" means that the physical observable remains bounded.

 

[PeterDonis]

If its origin is only partly geometric, as the paper argues using the cosmon field, then tidal gravity is no longer defined by geodesic deviation.

Ok, having looked at the paper some more, let me try to describe how this would have to work, based on the math in the paper.

In the standard cosmology model, the "spacetime geometry" term is $R \sqrt{g}$, where $R$ is the Ricci scalar and $g$ is the determinant of the metric tensor. (I'm using the paper's notation, which does not appear to be concerned with the sign of $g$; strictly speaking, the determinant $g$ is negative so the factor in the Lagrangian should be $\sqrt{-g}$ since that factor must be real, and that's how it will appear in most GR textbooks.)

In the paper's model, the corresponding term in the Lagrangian is $\chi^2 R \sqrt{g}$, where $\chi$ is the "cosmon" field. So if we view $R$ and $g$ as describing, not the actual physical metric (the thing that describes distances and times measured with physical rods and clocks), but a "background" metric that is not directly observable, then the paper's description of the model as describing a static spacetime in which masses continually increase (because the "Planck mass" in the model continually increases with $\chi$) makes sense, if we bear in mind that the "static spacetime" geometry is not the spacetime geometry that is directly observed; for example, the timelike geodesics of this background spacetime are not curves that describe the worldlines of objects with zero proper acceleration, and the curvature tensor derived from this background spacetime metric does not describe actual deviation of the worldlines of actual physical objects that have zero proper acceleration.

However, that then leaves the obvious question: what are the direct physical observables in the paper's model? As far as I can tell, this question is never directly addressed in the paper. We are never told, for example, how to describe the motion of a freely falling object--an object with actual, physical zero proper acceleration--in this model. What is its worldline? It isn't a geodesic of the "background" spacetime geometry, we know that. But we are never told what it is, except for the general statement that the model "represents the same physics" as standard cosmology. But if the model represents the same physics, then all physical observables should be the same, and that includes the physical observables that increase without bound as the Big Bang singularity is approached.

The paper's explanation of how the singularity gets removed is that the curvature scalar $R$ of the "background" spacetime geometry remains finite and bounded as $t \rightarrow - \infty$ (which corresponds to $t \rightarrow 0$ in the standard cosmology). But as we have just seen, that curvature scalar does not represent any physical observable. We are never told what, in the paper's model, does represent the relevant physical observable as $t \rightarrow \infty$ in the model, much less how such an observable remains finite and bounded--which, if the paper's claim that its model "represents the same physics" as standard cosmology is true, cannot be the case.

So I am still not convinced that the paper actually presents a solution that is free of physical singularities. As far as I can tell, the "field redefinition" trick just obfuscates the situation by making the unphysical "background" spacetime Ricci scalar stay finite and bounded, and then trying to ignore the fact that this scalar does not represent the actual relevant physical observable.

 

[jcap]

As far as a response to my response is concerned, the shell and everything inside it is still a gravitationally bound system, whether "space is expanding" outside it or not, so both models--standard cosmology and Wetterich's model--predict the same observations for the shell and inside it.

OK - I would be very interested in your response to the following idea to test a generic "shrinking matter" cosmology:

Imagine (sorry!) two massive similarly-charged objects at rest in space such that their gravitational attraction is exactly balanced by their electromagnetic repulsion.

The objects each have mass $M$, charge $Q$ and their separation is $d$.

Then in natural units ($\hbar = c = 4\pi\epsilon_0 = 1$, $G = 1/M_P^2$) we have:
$$\frac{1}{M_P^2}\frac{M^2}{d^2}=\frac{Q^2}{d^2}$$
Therefore
$$\frac{M}{M_P}=Q$$
Clearly this equation does not change with the universal scale factor $a(t)$ if $M \rightarrow M a(t)$ and $M_P \rightarrow M_P a(t)$.

Therefore I presume that the separation distance $d$ does not change and can be used as a reference to check whether atomic sizes do change.

Does this work?

P.S. I think the crucial difference between the scenario above and the gravitationally-bound orbit scenario in post #18 is that the bodies here have no angular momentum. An orbiting body has constant angular momentum $L=mvr$ ensuring that if $m \propto a$ then $r \propto 1/a$. (In natural units angular momentum and velocity are dimensionless.)

Post #18: https://www.physicsforums.com/threa...f-shrinking-matter-theory.993768/post-6394052

 

[PeterDonis]

I would be very interested in your response to the following idea to test a generic "shrinking matter" cosmology:

You can't test a "generic" cosmology. You have to test a well-defined mathematical model. You're not; you're just waving your hands and using intuitive reasoning that might or might not be valid for any mathematical model. You certainly have not shown that your intuitive reasoning is valid for the model described in the Wetterich paper.

 

[PeterDonis]

The actual model referenced in the OP has been sufficiently discussed, and speculation is off topic. Thread closed.