# Re: aiming to complete Everett's derivation of the Born Rule

`On Sun, Apr 24, 2022 at 9:09 PM Bruce Kellett <bhkellet...@gmail.com> wrote:`
```
> This is what Sean Carroll actually says in his book "Something Deeply
> Hidden":
>
> "*Well", replied Alice. "Just think about ordinary textbook quantum
> mechanics. Given a quantum state, we can calculate the total energy it
> describes. As long as the wave function evolves strictly according to the
> Schrodinger equation, that energy is conserved, right?" ....*
> *"Not all worlds are created equal. Think about the wave function. When it
> describes multiple branched worlds, we can calculate the total amount of
> energy by adding up the amount of energy in each world, times the weight
> (the amplitude squared) for that world. When one world divides in two, the
> energy in each world is basically the same as it previously was in the
> single world (as far as anyone living inside is concerned), but their
> contributions to the total energy of the wave function of the universe have
> divided in half, since their amplitudes have decreased. Each world got a
> bit thinner, although its inhabitants can't tell the difference.*" (page
> 173)
>
> In other words, Sean is saying that energy conservation works for the
> multiverse, and he implies that it also works in each individual branch.
> This is nonsense --  you can't have both. If energy is conserved over the
> multiverse, then it cannot be conserved in each branch separately,
>

Nonsense.  You can if, as Sean Carroll says you  "add up the amount of
energy in each world, times the weight (the amplitude squared) for that
world". I think you've forgotten your first year calculus, it's possible to
add up an infinite number of numbers and get a finite result.

>* Energy conservation is routinely observed and checked in individual
> branches.*
>

Correct.

* > No one has ever checked energy conservation in the multiverse.*
>

Correct again, there is no experimental confirmation that energy is
conserved in the multiverse, and it would violate no law of logic if it was
not, but most versions of Many Worlds assume energy is conserved.  And
nothing in the above contradicts what Sean Carroll said.

*> The idea that this energy is conserved in the multiverse derives from
> the observation that the Schrodinger equation is time translation
> invariant.*
>

With cosmology you can't assume Schrodinger's equation tells you all you
need to know because it says absolutely nothing about gravity and doesn't
include General Relativity. And we don't even know for a fact that the laws
of physics are time translation invariant, not if you're talking about
billions of years or a trillionth of a trillionth of a trillionth of a
second after the big bang during the era of cosmic inflation

* > The trouble with Sean's glib response to the question is that in each
> branch of the multiverse, we can measure the energy both before and after
> the supposed split.*
>

Neither before or after the split are you measuring the absolute total
energy in anything, in any energy measurement you're measuring the relative
energy of something against a standard measure. If you say a particle has X
units of energy calibrated against some standard measure, then after a
measurement (and thus after a split) if you want to measure the energy in
the decay products of the particle you do it by comparing them against the
same standard measure, but *that's impossible* because any act of
measurement splits a universe. So both the energy in the decay products and
the energy of the standard measure of energy are decreased by 1/2 (or by
however many times the universe splits), so you still get  X units of
Energy and the world still looks the same to you despite it having only
half the total absolute energy. It all comes down to the fact that you
never measure the absolute energy of something, you always measure the
relative energy.

> *If I want to check energy conservation in neutron decay, I compare the
> mass-energy of the original neutron to the sum of the mass-energies of the
> decay products plus any kinetic energy of these decay products.*

You left out a few steps. You compare the mass-energy of the original
neutron against a standard calibration measure, and then you measure the
mass-energies of the decay products plus any kinetic energy of these decay
products against a standard measure. If the energy of the decay products
and the energy of the standard measure have both been decreased by 1/2 then
you're going to get the same units of energy both before and after the
measurement.

John K Clark    See what's on my new list at  Extropolis