## Quantum Entanglement and the Many Worlds Interpretation

Erwin Schrödinger introduced quantum entanglement in a 1935 paper[1] delivered to the Cambridge Philosophical Society in which he argued that the state of a system of two particles that have interacted generally cannot be written as a product of individual states of each particle.

|Particle A interacting with B〉 ≠ |A〉|B〉

Such a state would be an entanglement of individual states in which one cannot say with any certainty which particle is in which state. Disentanglement occurs when a measurement is made.[2] This is what gave rise to Schrödinger’s famous (or infamous) cat illustration, which will be useful in understanding the role of measurement and the following consequent for a quantum version of many worlds.

The non-interactive state of two particles cannot be expressed as a certain conjunction of the two states. An example of an entangled state is

because a singlet is a zero spin particle and there are two possible outcomes for a particle’s spin—up or down. The first particle could be up, , or down, . When a measurement is made one of the possible states collapses and produces what is observed. After a measuring apparatus is introduced an unknown state,

the whole state becomes

Remember, the state above is just a function state in conjunction with a measuring apparatus. Such a state then evolves according to the Schrödinger equation

into a non-collapsed state

When the observer makes an observation the observer becomes entangled as well.

Schrödinger found this to be so incredibly “sinister” because when states are added to previous states for measurement, larger states of affairs, etc. anything and everything becomes entangled. Thus, it seems to be the case that the entire universe becomes one large state of entanglement.[3]

For the following example, consider the observer happy if a spin up is perceived. Let denote the observer’s state prior to measurement,

after perceiving spin up, and

after perceiving spin down. Using the Hamiltonian

which totals the energies involved in a given situation,[4] the measurement is to be described by the unitary Schrödinger time evolution operator

U will then clearly meet

Thus, in a non-collapsed state of entanglement an observer of the superposition

according to Everett, would appear as

and not as

It should be clear by that the conjunction of outcomes becomes actualized rather than one of the possible outcomes.[5]

[1] Erwin Schrödinger, “Discussion of Probability Relations Between Separated Systems,” Mathematical Proceedings of the Cambridge Philosophical Society 31 no. 4 (Oct. 1935).

[2] Jonathan Allday, Quantum Reality: Theory and Philosophy (Boca Raton, FL: Taylor & Francis, 2009), 374-75.

[3] Allday, 374-77.

[4] The formula for kinetic energy is , plus the expression V(x) denotes all the forms of potential energy possessed by the particle. Allday, 237.

[5] Max Tegmark, “The Interpretation of Quantum Mechanics: Many Words or Many Worlds?” arXiv:quant-phys/9709032v1 (Sep. 1997): 1-2.

### 4 Comments to “Quantum Entanglement and the Many Worlds Interpretation”

1. Max: You’re a brilliant guy, articulate and interesting. We all know its fun to speculate but this bowl holds no water. We could easily speculate anything in any universe irregardless of anything we find constant in this universe. What is the advantage to creating a bottomless pit of speculation, curiosity and time-wasting that does nothing to provide the truth of God, Jesus Christ, creation or the gospel that we don’t already have spelled out in far less academic terms. Who are you appealing to?

To me this is a cancer in our Christian apologetics gone malignant. This sort of reasoning expresses a brilliant mind that has lost its moorings in the gospel and is now adrift in abstractions that in this universe will probably amount to idle words.

I believe there are better uses for the mind. Yes, I admit my mind is not as capable as yours, nor do I understand the mathematics involved above; nevertheless I do have some inkling of the gospel and apologetics that red-flag this sort of apologetic as mostly showing off to other presumably smarter and high-rev Christian Apologists.

Again, as disagreeable as I may sound about this kind of apologetic, I hope to encourage you in making your apologetics valuable on a larger scale among many people that can benefit from your gifts.

• Tell me, Marvin, what do you find so abominable about MWI? Have you read my paper in which I depend the compatibility, and even attraction to the multiverse with theism? What have you read that makes you think these are incompatible or a “bottomless pit” of speculation? Actually, it’s not a bottomless pit and there’s little speculation involved here. It’s called inference to the best explanation and taking know premises, putting them together, and finding a plausible explanation for the data (particularly in the theological discussion). So, what *exactly* is your problem here?

If you’re concerned about the apologetic value (I’m not sure why it’s a concern at all, but okay) you can read my MA thesis on the multiverse and fine-tuning: http://digitalcommons.liberty.edu/masters/286/

If you’re concerned about theological ramifications please read this paper that was presented at EPS last year and is currently in review for their journal: http://sententias.org/wp-content/uploads/2010/02/EPS-Paper-God-and-the-Multiverse-PDF.pdf

2. Max: What I find abominable is the speculative nature of mulitverses. Have we any proof of another universe let alone many others? I’ve never heard of such a thing, and I’ve never seen anything written other than speculation and extrapolation. I will happily read your papers.

Since we dont seem to have any real evidence that there is another universe just outside the door of our own, it appears that all that is being done is speculating the number of angels on pin heads. Its a time waster and affords no one that I can see or know any relevant information that would turn someone to faith in Christ.

Maybe you should ask yourself if it is a legitimate apologetic concern to intermingle your theories and apologetics.

3. Max: I did read your paper on God and the Multiverse. What I found was exactly what I expected to see. It entailed a jump from the ground of old Greek philosophers to the hyperspace of extrapolated ideas that God has many universes because He’s big and great enough to make them. Not only am I not convinced but I am even more set against it. This venture into science fiction/religious fiction offers nothing we don’t already have in the most limited educational scenarios contained in this simple world.

Now, I admit, to those readers who are in your choir, they will no doubt pour praise upon this paper. But what are they praising? An infinite God? We have that without a mulitiverse. An omnipotent God? We have that without a multiverse. An Omniscient God? We have that without the mulitiverse. In effect, what you’ve done is add complication to abstraction and posit all as legitimate theory. The Multiverse theory of course does beg the question “why”?

The bible affirms nothing that you’ve written in your paper outside of the attributes of God. Transworld atonement? Doppelgangers? These seem to be missing in my bible text. If youre going to establish some necessity to holding to this mulitiverse theory, it needs to be grounded in some explicit text. I’d even take implicit ones if the context of scripture were describing ‘other worlds’ where the necessity of the atonement and doppelgangers were required for mirroring this world. But, then again, who says we are not the mirror and some other ‘real’ person is not the original? Ah the joys of speculative thinking…all is up for grabs and especially ‘reality’.

In my far less educated mind and no doubt far less capable; there is another reason for this theory and I am willing to wager it is because what is clear in scripture is being avoided for some reason. In short, this is a rabbit trail to remove the Christian mind from the obvious teachings of scripture to complex and abstract theories so that what is obvious is hidden by philosophy, reasoning and concepts that produce the answer you find more to your liking. Its just a guess…but who knows?

The telling statement is our inability to speak from any other basis than our own universe. The limitation of the human mind renders this apologetic mute. It may be that we can imagine a thousand universes and ten-thousand angels in a pin-head but where do we find the power to prove such imagination is actually a reality?

I’ll go one step farther; those old Greek philosophers didn’t have the revelation of the simplest Christian mind. They didn’t know anything as they should know and their theories and speculations were what Paul kicked to the curb in Colossians. To venture back to those philosophers and seek to inject then into our modern theology is a mistake of Thomas and now it seems we are making the same mistake. Don’t get me wrong, I appreciate the contribution of St. Thomas, I very much appreciate Anselm, I have their books too.

At best you’re concocting a piece-meal from old pagan philosophers, more modern theorist like Leibniz and spicing it up with some modern math and current speculations on the universe. In the end, I don’t have a clearer vision of Christ or God; instead I have increased questions based upon a theory forms its basis upon the vague ideas of pagan philosophers then Christianized with God’s attributes attached to it.

Obviously I am not a peer-review, I am a Christian brother who sees this issue quite differently than you.
My words may be against your theory, but my heart is for your success as an apologist and outstanding thinker. My sincere prayer is for your growth in grace and knowledge of our Lord and Savior Jesus Christ.