# Experimental test of shrinking matter theory?

• A
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?

Motore

phinds
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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
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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?

jbriggs444
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 and etotheipi
phinds
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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
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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
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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.

phinds
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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.

berkeman and phinds
phinds
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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
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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.

phinds
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pair of satellites orbiting Earth separated by a small distance
Like the "GRACE" experiment?

mfb
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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.

timmdeeg
PeterDonis
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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.

berkeman
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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.

phinds
Dale
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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.

phinds
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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.

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.

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.

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!

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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.

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Dale
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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
2019 Award
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.

mfb
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
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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.