Experimental test of shrinking matter theory?

[jcap]

Prof Wetterich has proposed that atoms are shrinking rather than the Universe is expanding.

Here is a 2013 Nature News article describing his theory:

https://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379

Here is his 2013 paper "A Universe without expansion":

https://arxiv.org/abs/1303.6878

He proposes that space is static but that all masses in the Universe grow due to interaction with the scalar "cosmon" field. This causes all atomic length scales to shrink with the Universal scale factor. Thus the expansion of the Universe is an apparent effect.

I was wondering if the theory could be tested in the following way:-

Consider a pair of satellites orbiting Earth separated by a small distance $d$ of say $100$ meters.

Assume both satellites use laser range-finding technology to continually measure the distance $d$ and send the data back to Earth.

If atomic scales are shrinking then the apparent measured value of $d$ should increase with the universal scale factor. After a year the change would be about $10^{-8}$ meters which should be easily detectable.

Would this work?

 

[phinds]

As I recall,"shrinking matter theory" has fatal flaws. Check out the links at the bottom of this page and / or do a forum search.

 

[berkeman]

As I recall,"shrinking matter theory" has fatal flaws. Check out the links at the bottom of this page and / or do a forum search.

But, but, a lot of those poster names have lines through them now. What does that mean?

 

[weirdoguy]

This causes all atomic length scales to shrink with the Universal scale factor.

And how would it explain that expansion happens only on very large scales where objects (groups of galactics) are not graviationally bound?

 

[phinds]

But, but, a lot of those poster names have lines through them now. What does that mean?

In the context of this thread I think it means you are inadvertently encouraging the OP to believe in a widely debunked theory.

 

[phinds]

And how would it explain that expansion happens only on very large scales where objects (groups of galactics) are not graviationally bound?

And how would you explain red-shift.

And on and on ...

 

[PeterDonis]

how would it explain that expansion happens only on very large scales where objects (groups of galactics) are not graviationally bound?

how would you explain red-shift.

You might want to read the paper linked to in the OP before asking such questions. Even if the model described in the paper is wrong, that doesn't necessarily mean it's wrong in a simple-minded way.

 

[PeterDonis]

Check out the links at the bottom of this page

Note that none of those links contain a reference to an actual paper that describes an actual model. This thread does. That does make a difference.

 

[phinds]

You might want to read the paper linked to in the OP before asking such questions. Even if the model described in the paper is wrong, that doesn't necessarily mean it's wrong in a simple-minded way.

Thanks Peter. I had just skimmed the abstract. The math in the article is beyond me but the article seems very solid to my limited knowledge. What do you think of it, particularly his conclusion?

 

[PeterDonis]

What do you think of it, particularly his conclusion?

I haven't had time to read through it yet. Will post an update after I have done so.

 

[Bystander]

pair of satellites orbiting Earth separated by a small distance

Like the "GRACE" experiment?

 

[mfb]

The model is basically just a re-definition of units. Take co-moving coordinates and the universe doesn't expand, but all gravitationally bound objects shrink because (by normal definitions) your length scale grows. The author goes one step further and changes some more constants to make that a bit less obscure on smaller scales but it's still the same idea.

You cannot test this in any way because it doesn't make predictions different from an expanding universe.

 

[PAllen]

Besides the Nature commentary in the OP, here is another contemporaneous blog discussion. Both the Nature commentary and this one are in agreement with @mfb ’s point above.

https://www.science20.com/hammock_physicist/universe_expanding_or_are_we_shrinking-118673

 

[PeterDonis]

You cannot test this in any way because it doesn't make predictions different from an expanding universe.

This can't be true if the author's claim that there is no singularity in his model, while there is in a standard Big Bang model, is correct. That all by itself is a difference in prediction, since it means a different spacetime geometry.

I have not finished the paper, but from what I have read so far it seems to me that, while the author would like to claim that his model is just a different view of the same physics (which is the position the articles reviewing it are taking, as @PAllen notes), which would indeed mean it makes the same testable predictions, the actual model he presents does not appear to be the same physics. As noted above, the author's model differs from at least some more standard models in cosmology in the absence of a singularity (although "eternal inflation" models also do not have one). The Lagrangian he presents also seems obviously different from the standard GR Lagrangian with a scalar field as the only matter present (since in the standard GR Lagrangian there is no scalar field coupling in the curvature scalar term--this is also true of the Lagrangians of standard "eternal inflation" models).

So it seems to me that this model should make at least some testable predictions that are different from those of standard cosmology. I suspect that any such predictions would be obviously ruled out by data we already have, which might be why the author of the paper would rather people view his model as just a different view of the same physics, instead of proposed different physics.

 

[PeterDonis]

This can't be true if the author's claim that there is no singularity in his model, while there is in a standard Big Bang model, is correct. That all by itself is a difference in prediction, since it means a different spacetime geometry.

Ok, I have read the rest of the paper, and the author tries to (IMO) obfuscate this point by calling what he is doing a "field redefinition" and claiming that the Big Bang singularity in standard models is a "field singularity", which he says is like a coordinate singularity in that it does not imply that any actual physical observable increases without bound.

But all of this appears to me to ignore an obvious point: the Ricci curvature scalar itself is a physical observable. And in standard models with a Big Bang singularity, the Ricci curvature scalar is what increases without bound as the singularity is approached. His "field redefinition" changes the value of the Ricci curvature scalar, and therefore changes a physical observable.

 

[Dale]

This is strange to me. On the one hand he explicitly states “The different pic- tures are equivalent, describing the same physics.” And on the other he claims no singularity in his cosmology. Those statements cannot both be true.

 

[PAllen]

I’ve been thinking about a way to understand the result. I have not read in enough detail to know this is true, but is my current best understanding.

First, note that transformations described modify the metric itself, not just coordinates. Imagine, for example, a surface with a cusp that is a curvature singular point, topologically a plane minus a point. This singularity is not removable with the given metric. Imagine modifying the actual geometry, exponentially reducing curvature. One ends with a flat plane missing a point. This can now be geodesically completed. Consider, in the 4d case, the expression of the laws of physics are modified to yield the same predictions as the geometry changes. If this picture is correct, the removal of the singularity is physically meaningless. It is only removed from the geometry used to express the physics, but not from the physics itself - there remains infinite initial density and tidal forces for a choice of parameters that produce this for the standard model.

 

[jcap]

And how would it explain that expansion happens only on very large scales where objects (groups of galactics) are not graviationally bound?

If two objects are not gravitationally bound then the real distance $d$ between them is constant. If the observer is shrinking then he will measure an apparent increase in distance $d$.

However consider an object of mass $m$ in a circular orbit with velocity $v$ around an object of mass $M$. The Newtonian equation of motion is given by:
$$\frac{mv^2}{r}=\frac{GMm}{r^2}$$
Now without loss of generality we can use natural units ($\hbar=c=1$) so that $G=1/M_P^2$ where $M_P$ is the reduced Planck mass.

Thus we have
$$\frac{mv^2}{r}=\frac{1}{M_P^2}\frac{Mm}{r^2}$$
$$r=\frac{M}{M_P^2v^2}$$

Now let us assume that the masses are increasing with the scale factor $a(t)$ so that $M\rightarrow Ma(t)$ and $M_P\rightarrow M_Pa(t)$. This implies that atomic sizes scale like $1/a(t)$. Note that in natural units the orbital velocity $v$ is dimensionless so it remains constant.

Thus if masses are increasing with scale $a(t)$ the radius $r$ of the orbit is given by
$$r=\frac{M}{M_P^2v^2a(t)}$$

Thus orbital distances decrease in the same way as atomic distances so that a shrinking observer does not detect any change in gravitationally bound systems.

 

[jcap]

And how would you explain red-shift.

And on and on ...

The model assumes that space is static but that the energy scale of all massive particles is increasing with the universal scale factor $a(t)$ due to interaction with an increasing universal scalar field.

Crucially the energy of massless particles like photons is constant.

Thus the redshifted photons we detect now are not due to space expansion but rather because the energy scale of the absorbing atoms now is higher than the energy scale of the same type of atoms emitting in the past.

 

[jcap]

Like the "GRACE" experiment?

Thanks for the info!

Apparently there have been satellite experiments that measure the distance between a pair of satellites while performing gravitational surveys of the Earth and Moon.

https://www.jpl.nasa.gov/missions/gravity-recovery-and-climate-experiment-grace/

Actually they say that the GRACE satellite survey has 15 years of data.

If the data consists of repeatedly measuring the distance between the satellites then maybe it shows a tiny increase in distance in between the “noise” of the actual survey!

Though more likely local gravitational conditions might completely swamp any effects due to cosmological scale changes.

I guess if one needs to be far from local gravitational influences one could use a solar orbit like the proposed LISA gravitational wave detector:

https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna

Then you've only got the occasional gravitational wave to worry about!

 

[jcap]

The model is basically just a re-definition of units. Take co-moving coordinates and the universe doesn't expand, but all gravitationally bound objects shrink because (by normal definitions) your length scale grows. The author goes one step further and changes some more constants to make that a bit less obscure on smaller scales but it's still the same idea.

You cannot test this in any way because it doesn't make predictions different from an expanding universe.

A co-moving light-clock would consist of light bouncing between two mirrors out in empty space. Round-trip light travel times to remote galaxies would be measured as constant by such a clock. Conversely round-trip light travel times to the end of a rigid rod made of atoms would decrease.

But we don't use co-moving rulers/clocks.

Our rulers/clocks are based on atoms.

If we consider a massive body like the Sun then the spacetime around it is described by the Schwarzschild metric which does not expand. The spacetime in the locality of a pair of orbiting satellites is Minkowski which also does not expand.

According to standard GR the round-trip light travel time measured by atomic clocks between a pair of orbiting satellites that are at rest with respect to each other should be constant even though the Universe at large is expanding.

But if there is a universal scalar field which changes atomic masses then, contrary to standard GR, the round-trip light travel time between the pair of satellites, measured by our atomic clocks, should change.

 

[Dale]

If the data consists of repeatedly measuring the distance between the satellites then maybe it shows a tiny increase in distance in between the “noise” of the actual survey!

Here is a presentation that explains how this data is actually interpreted:

https://earth.esa.int/documents/973910/1006684/RR3.pdf

 

[PAllen]

I’ve been thinking about a way to understand the result. I have not read in enough detail to know this is true, but is my current best understanding.

First, note that transformations described modify the metric itself, not just coordinates. Imagine, for example, a surface with a cusp that is a curvature singular point, topologically a plane minus a point. This singularity is not removable with the given metric. Imagine modifying the actual geometry, exponentially reducing curvature. One ends with a flat plane missing a point. This can now be geodesically completed. Consider, in the 4d case, the expression of the laws of physics are modified to yield the same predictions as the geometry changes. If this picture is correct, the removal of the singularity is physically meaningless. It is only removed from the geometry used to express the physics, but not from the physics itself - there remains infinite initial density and tidal forces for a choice of parameters that produce this for the standard model.

I now think the description of the Big Bang early state changes, but in a way claimed to be physically equivalent. Instead of energy density approaching infinite, the decreasing mass of everything as time is followed back means there is no infinite density. However, there is still a plasma state, including quark-gluon plasma, as atoms, then nuclei, then protons etc. get so big as to overlap. So it does seem to me that predictions can match standard cosmology model at any admissible time, without infinite density or a singularity in the mathematical spacetime of the model.

 

[jcap]

Here is a presentation that explains how this data is actually interpreted:

https://earth.esa.int/documents/973910/1006684/RR3.pdf

Thanks - it says the satellites were 200 km apart and the measurement sensitivity was 1 micron. I calculate that in a year there should be an effective increase in separation distance of about 10 microns if atomic length scales are inversely proportional to the scale factor. Apparently the satellites measured their relative velocity. Perhaps the separation distance could be calculated by integrating the relative velocity measurements.

 

[Dale]

Did you read to understand what the distance measurements are used to measure. The problem is that that thing will dominate the proposed measurement and the small effect will not be seen.

 

[jcap]

Did you read to understand what the distance measurements are used to measure. The problem is that that thing will dominate the proposed measurement and the small effect will not be seen.

Ok fair enough.

Perhaps the experiment would need to be in solar orbit like the proposed LISA gravitational wave interferometer experiment.

 

[PeterDonis]

So it does seem to me that predictions can match standard cosmology model at any admissible time

Only if you define "admissible time" as "any time at which the predictions match the standard cosmology model". Which looks to me like arguing in a circle.

Removing the singularity, as I said before, is a different testable prediction: it means that if we go far enough back along any comoving worldline, this model predicts that curvature invariants remain bounded, while the standard cosmology model with an initial singularity predicts that they increase without bound. I see no argument given in the paper for why making observations that far back should be intrinsically impossible. So it looks to me like the model in the paper does make different testable predictions from standard cosmology (although testing them would be extremely difficult in a practical sense with our current observational capabilities), even if the author of the paper doesn't want to admit it.

 

[PeterDonis]

Thus orbital distances decrease in the same way as atomic distances so that a shrinking observer does not detect any change in gravitationally bound systems.

if there is a universal scalar field which changes atomic masses then, contrary to standard GR, the round-trip light travel time between the pair of satellites, measured by our atomic clocks, should change.

You are contradicting yourself in these two statements. The satellites are part of a gravitationally bound system, which means, by your first argument, that the round-trip light travel time between them as measured by our atomic clocks should not change.

To be clear, I think, as I said just now in response to @PAllen, that the model in the paper does make testable predictions that are different from standard cosmology; but I also think that @PAllen is correct that none of those different predictions will show up in any regime we have actually tested so far. They will only show up if we are at some point able to make observations sufficiently far back in time to where a standard Big Bang cosmology with an initial singularity would predict curvature invariants increasing without bound where the model in the paper wouldn't. That will require making observations of conditions prior to inflation, which we are unable to do now and for the foreseeable future. But perhaps some day we will be.

 

[PeterDonis]

Perhaps the experiment would need to be in solar orbit like the proposed LISA gravitational wave interferometer experiment.

This would still be in a gravitationally bound system, so the point I made in my previous post just now would still apply.

 

[PAllen]

Only if you define "admissible time" as "any time at which the predictions match the standard cosmology model". Which looks to me like arguing in a circle.

Removing the singularity, as I said before, is a different testable prediction: it means that if we go far enough back along any comoving worldline, this model predicts that curvature invariants remain bounded, while the standard cosmology model with an initial singularity predicts that they increase without bound. I see no argument given in the paper for why making observations that far back should be intrinsically impossible. So it looks to me like the model in the paper does make different testable predictions from standard cosmology (although testing them would be extremely difficult in a practical sense with our current observational capabilities), even if the author of the paper doesn't want to admit it.

I think predictions match everywhere covered by both models, i.e. excluding the singularity of the standard model, which is not actually part of the manifold.

Note that curvature invariants are strictly measurable only with with mathematical instruments, a distinction which can be ignored in ordinary circumstances. If one brings in a theory of matter, and requires measurements to be made by material instruments, curvature invariants are no longer directly measurable. Consider the example of asymptotically infinite tidal gravity. This then translates to asymptotically infinite rate of convergence (in the case of Ricci curvature) of initially parallel nearby world lines. This is a statement about local acceleration, when viewed physically in terms of particles. However, the same asymptotically infinite mutual acceleration can be achieved in asymtotically flat spacetime with asymptotically finite interaction force applied to asymptotically 0 masses. Thus the material observable remains unchanged as the geometric curvature of the model is reduced arbitrarily.

This is how I interpret the section on the relation of the metric g’ versus g. This is not a coordinate transform. Instead, it is a change of geometry with corresponding change of matter fields to produce identical predictions.

 

[PeterDonis]

I think predictions match everywhere covered by both models, i.e. excluding the singularity of the standard model, which is not actually part of the manifold.

I don't think so. Since in the model in the paper, all curvature invariants are bounded, there must be a finite portion of the manifold in the standard cosmology model, a finite region "around" the singularity which is part of the manifold, where curvature invariants in the standard model exceed whatever bound there is in the model in the paper on those invariants. In that finite region, testable predictions will differ between the two models. The difference cannot be confined to just the singularity itself.

If one brings in a theory of matter, and requires measurements to be made by material instruments, curvature invariants are no longer directly measurable.

That just means the actual measurable predictions will be of invariants associated with the matter, such as the energy density. Those will have to increase without bound in the standard model, but be bounded in the model described in the paper, so the same argument I made above applies to them.

the same asymptotically infinite mutual acceleration can be achieved in asymtotically flat spacetime with asymptotically finite interaction force applied to asymptotically 0 masses.

No, this cannot duplicate tidal gravity, because the geodesics don't deviate. Tidal gravity is geodesic deviation; it is deviation of worldlines that have zero proper acceleration. Worldlines that deviate due to a mutual interaction force will have nonzero proper acceleration, and this will be a measurable difference.

it is a change of geometry with corresponding change of matter fields to produce identical predictions.

I agree that this is what the paper appears to be claiming when it talks about a "field redefinition". I just don't think that claim is correct for the entire spacetime, for the reasons given above. But it may be correct for the region of spacetime in our actual universe that we have actually been able to observe up to now.

 

[PAllen]

No, this cannot duplicate tidal gravity, because the geodesics don't deviate. Tidal gravity is geodesic deviation; it is deviation of worldlines that have zero proper acceleration. Worldlines that deviate due to a mutual interaction force will have nonzero proper acceleration, and this will be a measurable difference.

I disagree. Geodesic deviation is the model of tidal gravity assuming it is purely geometric in origin. 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. The only direct observable is convergence of particles with some initial state of motion. As long as you have a field that preserves the principle of equivalence, there need be no geometric analog. This seems similar to graviton theory on Minkowski space where you can treat the ‘real’ spacetime as flat, even though measurements are all consistent with the curved spacetime model.

 

[PeterDonis]

Geodesic deviation is the model of tidal gravity assuming it is purely geometric in origin. 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.

I am not getting that from the paper, but I have not tried yet to go into great detail about the "field redefinition" that it is claiming to perform.

 

[jcap]

You are contradicting yourself in these two statements. The satellites are part of a gravitationally bound system, which means, by your first argument, that the round-trip light travel time between them as measured by our atomic clocks should not change.

OK - fair enough.

Imagine a massive hollow spherical shell out in space. Inside the metric is flat Minkowski space by the corollary to Birkhoff's theorem.

Imagine two spacecraft at rest inside the hollow shell measuring their separation distance using laser range finding techniques. To be more specific assume that the separation distance is measured between the centers of mass of the two spacecraft .

According to standard GR the spacecraft measure a constant separation distance even though the space outside the shell is expanding.

According to Wetterich's theory the space both inside and outside the shell is static. But his theory implies an increasing universal scalar field which causes all matter to shrink. Thus the hollow shell will shrink around its center of mass. The two spacecraft inside the shell will also shrink around their respective centers of mass. But the separation distance between the centers of mass of the two spacecraft should remain constant. As the atomic clocks used by the spacecraft are increasing in frequency this means that the spacecraft will measure an apparent increase in the separation distance.

 

[eltodesukane]

When we talk about the universe expanding, we mean the ratio (galaxy distance/galaxy size) is increasing. We use the scale factor a(t) to represent this. Whether (galaxy distance is increasing) or (galaxy size is decreasing) is equivalent. All we know is the ratio.