The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

can see the ones that I can see.

our laws of physics must also say that every object carries within it information about which instances of it could interact with which

instances of other objects (except when the instances are fungible, when there is n...

entanglement info...

under certain circumstances, the laws of motion allow histories to rejoin (becoming fungible again).

This is the time-reverse of the splitting (differentiation of history into two or more histories) that I have already described, so a natural way to implement it in our fictional multiverse is for the transporter to be capable of undoing its own history-splitting.

In an interference phenomenon, differentiated histories rejoin.

the presence of the Y-history interferes with what the transporter usually does to an X-history. Instead, the X and Y histories merge.

Interference is the phenomenon that can provide the inhabitants of the multiverse with evidence of the existence of multiple histories in their world without allowing the histories to communicate.

rejoining take place only if no wave of differentiation has happened.

interference can happen only in objects that are unentangled with the rest of the world.

two applications of the transporter have to be ‘in quick succession’.

object in question has to be sufficiently well isolated for its voltages not to a...

If an object is unentangled, it can be made to undergo interference by something acting on it alone.

entangled objects, further splitting happens instead of interference.

When two or more values of a physical variable have differently affected something in the rest of the world, knock-on effects typically continue indefinitely, as I have described, with a wave of differentiation entangling more and more objects.

If the differential effects can all be undone, then interference between those original values becomes possible again; but the laws of quantum mechanics dictate that undoing them requires fine control of all t...

decohe...

decoherence is very rapid, which is why splitting typically predominates over interference, and why interference – though ubiquitous on microscopic scales – is quite hard ...

quantum interference phenomena constitute our main evidence of the existence of the multivers...

If a photon is introduced travelling rightwards (X) after the first mirror instead of before as shown, then it appears to emerge randomly, rightwards or downwards, from the last mirror (because then, happens there). The same is true of a photon introduced travelling downwards (Y) after the first mirror. But a photon introduced as shown in the diagram invariably emerges rightwards, never downwards.

one photon is ever present per history, because only one of those detectors is ever observed to fire during such

the fact that the intermediate histories X and Y both contribute to the deterministic final outcome X makes it inescapable that both are happening at the intermediate time.

In the real multiverse, there is no need for the transporter or any other special apparatus to cause histories to differentiate and to rejoin. Under the laws of quantum physics, elementary particles are unde...

histories may split into more than two – often into many trillions – each characterized by a slightly different direction of motion or difference in other physical v...

in general the resulting histories have un...

rate of growth in the number of distinct histories is quite mind-boggling

Because of this rejoining, the flow of information in the real multiverse is not divided into strictly autonomous subflows – branching, autonomous histories.

they are intimately affecting each other, because the effect of interference on a history depends on what other histories are present.

Not only is the multiverse no longer perfectly partitioned into histories, individual particles are not perfe...

Because these two groups of instances of the particle, initially at different positions, have gone through a moment of being fungible, there is no such thing as which of them has ended up at which final position.

during a collision between two atoms, the histories of the event

split into something like this and something like this

for each particle individually, the event is rather like a collision with a semi-silvered mirror. Each atom plays the role of the mirror for the other atom.

But the multiversal view of both particles looks like this

For the same reason, there is no such thing as the speed of one instance of the particle at a given location. Speed is defined as distance travelled divided by time taken, but that is not meaningful in situations where there is no such thing as a particular instance of the particle over time.

Instead, a collection of fungible instances of a particle in general have several speeds – meaning that in general they will do different things an instant later.

(This is another instance of ‘diversity withi...

Not only can a fungible collection with the same position have different speeds, a fungible group with the same speed can have different positions. Furthermore, it follows from the laws of quantum physics that, for any fungible collection of instances of a physical object, some of their attributes must be diverse. This is k...

an individual electron always has a range of different locations and a range of different spee...

at times and places where there are histories, it exists in instances which can never collide.)

If a particle’s range of speeds is centred not on zero but on some other value, then the whole of the ‘ink blot’ moves, with its centre obeying approximately the laws

of motion in classica...

put a proton into the middle of that gradually spreading cloud of instances of a single electron. The proton has a positive charge, which attracts the negatively charged electron. As a result, the cloud stops spreading when its size is such that its tendency to spread outwards due to its uncertainty-principle diversity is exactly balanced by its attraction to the proton.

Historically, this explanation of what atoms are was one of the first triumphs of quantum theory, for atoms could not exist at all according to classical physics.

Neither the nucleus nor the electrons individually have more than one ten-thousandth of the diameter of the atom, so what keeps them so far apart? And what makes atoms stable at that size?

the electron in its lowest-energy state is not orbiting at all but, as I said, just sitting there like an ink blot – its uncertainty-principle tendency to spread exactly balanced by the electrostatic force.

the phenomena of interference and diversity within fungibility are integral to the structure and stability of all static objects,

including all solid bodies, just as they are integr...

When an electron has more than one speed or more than one position, that has nothing to do with anyone being uncertain what the speed is, any more than anyone is ‘uncertain’ which dollar in their bank account belongs to the tax authority. The diversity of attributes in both cases is a physical fact, independent of what anyone knows or feels.