Can you exist in a scaled up universe?

Question

In this multiverse system, scaled down universes can be created by confining energy into a space with scaled down physical constants in proportion to the energy put in. Miniature universes of different sizes are capable of forming into a complex life-bearing universe.

Although each universe only contains a portion of its parent universe’s energy, because the physical constants are changed, the universe will have an equivalent amount of energy and any life forms that may evolve will have access to the same amount of energy in their universe as their creator does in theirs. They will also have to face the same troubles, such as expansion.

An expanding miniature universe can be anywhere from just smaller than the host universe to as small as a sub atomic particle depending on how much energy was used but my story will focus more around planetary/star sized universes.

Since every universe occupies the same space, with some sort of tremendous FTL method you could jump outside of your universes boundary and you will be in your makers scaled up universe but could you exist with your miniature particles? If every universes energy is the same single force but set at different distance/strengths for each scale, could smaller life-forms/objects (stable in their universe) survive in a scaled up universe?

Although the premise of scaling down subatomic particles and changing the physics constants is likely impossible, if it was possible, would the structure of a larger universe allow objects made from mini universe particles to exist within it?

Answer 1

Intro

You don't want to change the fundamental constants at least not without change the laws of physics, our current universe (with life) only exists because the physical constants are the way that they are. What will follow is an explanation of what is known as the "fine-tuned" property of our universe.

All physical constants to one degree or another play a role in the observable universe. The most important of these relate to the strong interaction, the gravitational interaction and the electromagnetic interaction.

The first two (strong interaction and gravitational interaction) are necessary for long term formations of planetary systems and star systems. The electromagnetic interaction is important for day-to-day phenomena which directly includes life.

The electromagnetic interaction

Lets exam the electromagnetic interaction since that would affect us on a day-to-day basis. There is a physical constant known as the Fine-Structure constant and it is shown below:

$\alpha = \frac{e^2}{4\pi\epsilon_0 hc} \approx 1.44 \ MeV \ fm$

Now what were to happen if this constant changed?

Since this constant depends on $\pi$, $\epsilon$ the vacuum permittivity, c the speed of light, and h or Planck's constant linearly then any change to these quanities will be reflected in the final outcome. If e, or the elementary charge unit, changes the outcome will be reflected in a squared manner. But these quantities are related to make matters more complicated. Lets just look at an example:

This constant affects the electrostatic force between particles and hence just about everything dealing with the electromagnetic interaction. If c is increased by say 1 percent, then the vacuum permittivity will be increased by 10 percent and the electrostatic potential energy between two electrons will be reduced by 10 percent and the ground state of hydrogen is reduced by about 20%! This means that all atomic bonds are much much weaker. Biochemistry is very delicate and could not exist if chemicals bonded much weaker and less frequently.

So lets say you try to salvage your universe by increasing the fundamental electric charge by 5 percent. Now the energy in a two-body system bound by the electric potential behaves like it should...except it doesn't. Only the electric potential energy looks right, now the electric potential is off as are the spacings in the energy levels of atoms and the energies of emitted photons. To make matters much worse, previously weak magnetic effects are now much more predominate, since the magnetic force has increased by over 15%!

And the process would continue...

Fine-tuning

Dr. Rees made a list of six constants which if affected at all would make life in any form we know it, impossible. The list can be found here ( https://en.wikipedia.org/wiki/Fine-tuned_universe ) and its important to keep in mind they are not fundamental physical constants.

To answer the question in your scenario, what would happen if you simply scaled up the universe: increased the length dimensions proportionally, and scaled the physical constants to match the new length scales. In this case, a very different thing is happening than changing the physical constants in relationship to one another. The new universe would behave exactly like ours because everything is still the same, the new lengths are purely in relationship to the old and are completely independent. The laws themselves haven't changed.

For instance the law of gravitation:

$F_{g} = G \frac{m M}{r^3} \vec{r}$

Here it doesn't matter if "r" is in meters or kilometers.

So if all length scales were replaced with kilometers, the fundamental laws wouldn't change. You might be wondering about quantum mechanics, but the Uncertainty principle would still be:

$\Delta_{x} \Delta_{p} \ge \frac{h}{2}$

Here, if x was in km as the standard unit, h would be have a value of 6.626... $\cdot 10^{-31} \frac{kg (km)^2}{s}$.

Thus as long as the "finely tuned" constants are not affected in relationship to one another, life in your new Universes could exist just fine with some small caveats.