the quantum conspiracy

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The Quantum Conspiracy

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The Quantum Conspiracy: What Popularizers of QM Dont Want You to KnowRon Garret 6 January 2011

Disclaimers The title of this talk is intended as ironic humor. There is no conspiracy (as far as I know :-) IANAPhysicist This talk is about a way to think about QM that hasnt gotten much attention

No one understands quantum mechanics. Richard Feynman

What does it mean to measure something?

Measurements are consistent across space and timeT0: Its Green! ? T1: Yep, its Green!

The most incomprehensible thing about the universe is that it is comprehensible Albert Einstein

A deep mystery It could be that measurements are consistent across space and time because there is an underlying (meta-) physical reality out there which is being accurately reflected But it turns out we can demonstrate that this is not so

Road map Step 1: Review the usual QM story Step 2: Show how it leads to a contradiction Step 3: Do some math and show how that resolves the contradiction Step 4: Tell a new story based on the math Step 5: Profit!

Quantum mystery #1 The two-slit experiment

Two-slit experiment results

Wave s

Particle

This is not intractably weird (yet) Light (and electrons) might be particles that are moved around by an underlying wave Randomness might be due to hidden variables But we can eliminate this possibility

Adding detectors to the slits

No detectors ==> interference

Detectors ==> no interference

Wave-particle duality Any modification to the experiment that allows us to determine even in principle which slit the particle went through destroys the interference Conclusion: something must be at both slits at once to produce interference This holds for any particle and any measurement (and any two-slit or split/combine experiment)(Aside: wave-particle duality is an inherent aspect (indeed part of

This is still not intractably weird Maybe measurement does something to the system to make it stop behaving like a wave and start behaving like a particle Maybe the wave collapses and becomes a particle (Copenhagen interpretation) But how and, more importantly,

Quantum mystery #2 The Quantum EraserReflec t Particl e Sourc e Split Com bine 0 Interferenc e 1 Reflec t

Quantum mystery #2 The Quantum EraserMeasure Particl e Sourc e Split Com bine 0. 5 Interferenc e destroyed 0. 5

Measure=rotate 90

Quantum mystery #2 The Quantum EraserMeasure Particl e Sourc e Split Erase Com bine Erase 0 Interferenc e restored 1

Measure=rotate 90 Erase=filter at 45

Shroedingers Cat When (and where) does collapse happen? At the measurement site? At the detector? In the mind? (Whose mind?)

Quantum mystery #3: Entanglement

Quantum EntanglementLU UV laser & DownConverte r R U Spl it LD LU/RD and LD/RU are perfectly correlated (because of conservation laws) Spl it R D

Spooky action at a distance Particle isnt really at either detector until it is actually measured (whatever that means) When an aspect of one photons quantum state is measured, the other photon changes in response, even when the two photons are separated by large distances. (Wired, June 2010)

Now its intractably weird! Instantaneous effects are supposed to be impossible! Randomness precludes transmitting information using entanglement Or does it?

Road map Step 1: Review the usual QM story Step 2: Show how it leads to a contradiction

Taking stock A split/combine experiment produces interference Any which-way measurement destroys interference Some which-way proto measurements can be erased, restoring interference Measurements on entangled particles are perfectly (anti)correlated

Taking stock A split/combine experiment produces interference Any which-way measurement destroys interference Some which-way proto measurements can be erased Measurements on entangled particles are perfectly (anti)correlatedWhat they dont want you to know:

All of these things cannot possibly be true!

The EPRG* Paradox

*Einstein-Podolsky-RosenGarret

The EPRG* Paradox

If we measure on the left, do we destroy interference on the right?

The EPRG Paradox If the answer is yes then we have FTL communications But if the answer is no then we know the position of the particle but we have interference nonetheless, which violates QM

One last possibility Maybe there was no interference to begin with! Maybe entanglement counts as a protomeasurement that destroys interference But then we can do FTL communications by creating interference with a quantum eraser! Conclusion: either FTL communications is possible, or something in this story is wrong

Road map Step 1: Review the usual QM story Step 2: Show how it leads to a contradiction Step 3: Do some math and show how that resolves the contradiction

Math (dont panic) (x,t) is the quantum wave function Complex-valued function of space and time Evolves according to the Schroedinger wave equation

| (x,t)|2 is the probability of measuring a particle at position X at time T

Things to note about the math Distinguishes between amplitudes (complex numbers) and probabilities (real numbers) Particles can interfere because complex numbers with modulus greater than zero can add to zero.

Continuous, time-symmetric, fully deterministic (and hence reversible) dynamics No randomness, no collapse. Going from amplitudes to probabilities has no physical justification. Its purely a hack. (But it works!)

Two-slit mathState of the photon without measurement: ( + U )/2 L (Note the 2. It will be important later.) Resulting probability (| | ): 2 2 * * [| U | + | L| + ( U L + L Interferenceterm2

U

)]/2

Two slits with detectorsProbability amplitude: ( |DU> + U |DL>)/2 L(|DU> is the amplitude of the detector indicating a particle at the upper slit)

Two slits with detectorsProbability amplitude: ( |DU> + U |DL>)/2 L(|DU> is the amplitude of the detector indicating a particle at the upper slit)

Resulting probability:[| (* U

|2 + | U* L

|2 + LU

+ L

)]/2

Two slits with detectorsProbability amplitude: ( |DU> + U |DL>)/2 L(|DU> is the amplitude of the detector indicating a particle at the upper slit)

Resulting probability:[| (* U

|2 + | U* L

|2 + LU

+ L

Interference term (!)

)]/2

Measurement and interference is the amplitude of the detector switchingspontaneously from the U state to the L state If the detector is working properly, this amplitude is 0 Then the resulting wave function is:

(|

|2 + | U

|2)/2 L

Note: no interference term!

Measurement is a continuum!

Entangled particles Wave function: (| > + | >)/2 Equivalent to: (| >| > + | >| >)/2 (|LU>|RD> + |LD>|RU>)/2 ( LU |RD> + LD |RU>)/2 which should look familiar.

Entanglement and measurement are the same Wave function of entangled particles is phenomenon! exactly the same as a measuredparticle They are in fact the same physical phenomenon (more on this in a moment) There is no interference in the EPRG experiment But can we create interference with a

Quantum eraser revisitedMeasure Particl e Sourc e Split Erase Com bine Erase

0 Interferenc e restored 1

Measure=rotate 90 Erase=filter at 45

Quantum eraser math Wave function after measurement (but before erasure): (|U>|H> + |L>|V>)/2 Wave function after erasure: (|U> + |L>)(|H> + |V>)/22|H> + |V> means polarized at 45

|V >

|H> + |V>

|H >

Quantum eraser math Before erasure: no interference After erasure: interference but Remember that 2 term? Its there to make the total probability come out to 1. But the total probability isnt 1, its 1/2! Either weve made a mistake, or half our photons are missing

Quantum eraser math Half of our photons have gone missing! They were filtered out Filtered photons have a different wave function: (|U> + |L>)(|H> - |V>)/22|V >|H> + |V>

|H >|H> - |V>

So much for our Nobel prize Photons that pass through the filter display interference fringes Photons that dont pass through the filter also display interference anti-fringes Sum together to produce non-interference So quantum erasers dont erase anything, and they dont produce interference, they just filter out interference that was already there

Filtering out interference in an EPR experimentUDUDD

Select U photons + D

=

Road map Step 1: Review the usual QM story Step 2: Show how it leads to a contradiction Step 3: Do some math and show how that resolves the contradiction Step 4: Tell a new story based on the math

Interpretations of QM Copenhagen (scientifically untenable) Relative-state (Multiple worlds, Decoherence) Scientifically tenable but intuitively troublesome

Transactional (Cramer) Physically real waves moving backwards in time (predicted by Maxwells equations)

Quantum information theory (Zero-worlds) Extension of classical information theory with complex numbers

Classical Information TheoryShannon entropy of system A: H(A) = P(a) log P(a)

P(a) is probability that A is in state a H(A) is a measure of the randomness of system A When system has equal probability of being in one of N states, H(A) is log(N) When N is 1 (system is definitely in a single state) H(A) = 0

Classical Information theory Joint entropy of multiple systems: H(AB) = - p(ab) log p(ab) Conditional entropy: H(A|B) = - p(a|b) log p(a|b) Information entropy:I(A:B) = I(B: