[SEQ RERUN] Spooky Action at a Distance

MinibearRex

Today's post, Spooky Action at a Distance: The No-Communication Theorem was originally published on 05 May 2008. A summary (taken from the LW wiki):

As Einstein argued long ago, the quantum physics of his era - that is, the single-global-world interpretation of quantum physics, in which experiments have single unique random results - violates Special Relativity; it imposes a preferred space of simultaneity and requires a mysterious influence to be transmitted faster than light; which mysterious influence can never be used to transmit any useful information. Getting rid of the single global world dispels this mystery and puts everything back to normal again.

Discuss the post here (rather than in the comments to the original post).

This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Bell's Theorem: No EPR "Reality", and you can use the sequence_reruns tag or rss feed to follow the rest of the series.

Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.

Today's post, Spooky Action at a Distance: The No-Communication Theorem was originally published on 05 May 2008. A summary (taken from the LW wiki):

As Einstein argued long ago, the quantum physics of his era - that is, the single-global-world interpretation of quantum physics, in which experiments have single unique random results - violates Special Relativity; it imposes a preferred space of simultaneity and requires a mysterious influence to be transmitted faster than light; which mysterious influence can never be used to transmit any useful information. Getting rid of the single global world dispels this mystery and puts everything back to normal again.

The wave function is a scalar in the regular QM, so it is unchanged under the Lorentz transformations.

Eh? If I have a scalar field phi(x) in classical physics and I rotate the universe by pi/2 (an active transformation) the field not changes to phi(Mx) where M is the linear map that rotates the universe by pi/2 in the other direction. This changes phi, no? I know that if phi were a vector field then we would have the additional change that the vector rotates as well (i.e. we get M^(-1) v(Mx)), but the scalar field phi still in some sense changes.

If I wanted to check if my theory was invariant by rotations by pi/2 I would take a field that satisfied my equations, apply the above transformation to it, and see if it still satisfied my equations. What analogous transformation could I apply to a wavefunction to check if my theory was Lorentz invariant?

(Also, isn't the wavefunction also a scalar in QFT?)

This changes phi, no?

Definition of a scalar). In other words, if you change your coordinate system, a value of the scalar field at a given point in spacetime (now described by the new coordinates) is still the same number. Whereas a vector will, in general, have different components.

(Also, isn't the wavefunction also a scalar in QFT?)

No. To quote wikipedia, "probability conservation is not a relativistically covariant concept", because the particle number is neither conserved, nor is a covariant quantity. I.e., different observers can disa... (read more)

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