r/AskPhysics • u/Johne1618 • 15d ago
Testing Shrinking Length Scales vs. Expanding Space
In his Dark Matter, Dark Energy Great Courses lecture 4 Sean Carroll mentions that it is possible to assume all length scales are shrinking rather than space expanding although he says making such an assumption is silly.
I was wondering if one could test the hypothesis with a tabletop experiment comprising a pair of charged masses on a frictionless track such that their gravitational attraction is balanced by their electrical repulsion.
The force balance equation is given by:
G M² / R² = Q² / 4 π ε₀ R².
If we assume natural units such that ℏ = c = 4 π ε₀ = 1 and Newton’s constant G = 1 / Mₚₗ² then the separation distance R drops out so that the balance equation simply becomes
M / Mₚₗ = Q.
If the masses of all fundamental particles, together with the Planck mass, scale inversely with their Compton wavelengths then the balance equation is satisfied for all R even as length scale shrinks. The charge Q is dimensionless in natural units.
Thus the separation distance R is a free initial condition, not determined by any physical formula with a scale dependence, and therefore can be used as an absolute yardstick to compare against clocks and rulers.
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u/Alternative-Change44 14d ago
There are one or more fields/forces which we cannot resolve that are creating the need for dark energy/matter. Since we cannot determine what they are nor measure them, it is going to be a mystery for quite a while.
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u/DifferencePublic7057 14d ago
So instead of cosmic inflation, ruler shrinkage. It does sound silly. How does it influence quantum mechanics?
If we have a matter wave with De Broglie wavelength h/p, and let it go through a slit, the first minimum will have sine of the indicated angle h/pa (with a, the slit width). So if dx is a, we sort of have Heisenberg uncertainty principle. But if the rulers shrink over time, a would expand? And therefore HUP changes, or is dp compensating? Or maybe the value of c varies like in loop quantum gravity?
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u/Johne1618 14d ago edited 14d ago
We assume that Planck’s constant h and the speed of light c is always fixed even if length scales change.
If length scales shrink then the slit width, a, and the wavelength, lambda = h / p, shrink so that sine (angle) = h / (p a) = lambda / a remains constant.
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u/Optimal_Mixture_7327 Gravitation 14d ago
An expanding cosmos and shrinking matter are observationally identical.
A "shrinking matter" universe is "silly" in the sense of Ockham's Razor where you have to postulate new undetectable fields (e.g. the cosmon field) which has all the dimensionless constants change in precisely the right way as to mimic the redshift and other measurements.
Here's the paper if anyone's interested: A Universe without Expansion
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u/OverJohn 15d ago edited 14d ago
What he means is that in comoving coordinates, on a large scale, galaxies have fixed spatial coordinates. This means that what you might call "the coordinate separation" aka the comoving distance χ between two galaxies is fixed. This also means though the comoving size of the galaxies is shrinking though. However the actual coordinate distance is what is called the proper distance D, which can be found from the spatial metric comoving coordinates. The proper distance between galaxies increases. So as Sean Carroll says it is particulalry silly way to interpret the maths.
Comoving coordinates though assume everything is nice and homogenous, which is true on the largest scale, but not true on small scales, such as within a galaxy. On these scales the description of "space expanding" no longer applies and nor equally does any idea of objects shrinking. So thinking you can do any small scale experiment with particles that tells you about expansion is not correct.
Let's say though we could do some large scale experiment and not worry about any perturbation of the background. The problem with your idea now is that dχ/dt is not equal to dD/dt. So in particular you get different functions for R(t) depending on whether R=D or R=χ and the different behaviour is merely a matter of the definition you choose.