SEVEN DEADLY QUANTUM SINS

C. S. UnnikrishnanFundamental Interactions Laboratory

Tata Institute of Fundamental Research,Mumbai 400005tifr.res.in/~filab

The truncated list:

1.Quantum Muddle Identifying the physical system with the state/w-function 1b) What exactly is a Schrodinger Cat?

2.Uncertainty principle, disturbances and measurements on single systems

3.What exactly is the EPR argument as meant by Einstein?

4.Bell’s inequalities and theories of correlations

5.Do experimental results indicate (let alone ‘prove’) nonlocality? Entanglement=Nonlocality?!

6.The belief of the reality of zero-point modes in vacuum

7.Black holes and information loss – serious misunderstanding of black hole gravity

There are other ones…

1)(Fact )Present quantum theory requires the assumption that QM is NOT applicable to all physical systems

2)(Belief) Decoherence solves the problem of ‘quantum to classical transition’

3)…

1. THE QUANTUM MUDDLE

Quantum system = Quantum state, physically.

(Wavefunction = Particle and wavefunction has a space-time existence)

1. The Quantum Muddle

The notion arose from peculiarities of single particle quantum mechanics and wave-particle duality.

( ) 1( ) 2( )z z z ‘Photon’ interferes with itself…

Particle is in both paths….

1

2z z

Of course, it will be a severe mistake if one interprets this state as the particle being both up and down at the same time, because the state is

1

2z z x

An individual physical system in classical physics might be an element of an ensemble with a probability distribution for its observables – however it will be silly to identify the individual with the distribution.

Local detection, ‘Collapse of the wavefunction’ etc.

What is the ontological description one has in mind?

This of course leads to severe confusion of nonlocality. However the serious problem has been in relation to Schrodinger cat and entanglement.

Quantum muddle and the Schrodinger cat:

1, ,

2Atom Cat Atom Cat

1

2cat Cat Cat

Imagine describing an electron in a superposition of up and down spin projection states and an electron spinning both up and down! Quantum mechanically it has a spin projection orthogonal (geometric) to being up or down.

1 2 1 2

1

2

Schrodinger would have been appalled to know that this state of elementary particle is also called by many as a S-cat!

2. Uncertainty principle, disturbances and measurements on single systems

/ / 2p h h x

Suppose there was only ONE which-way sensor:

Interference is still washed out 100%! So, vanishing of interference and coherence has nothing to do with disturbance of momentum transfer.

Can one measure the position and momentum of a particle more accurate than allowed by the uncertainty relation ?

Source slit and detector resoltuion x

What is the resolution of momentum determination?

After a large number of measurements, what is the position uncertainty?

3. What exactly is the EPR argument as meant by Einstein?Excerpts from Einstein’s letter to Popper (reproduced in Logic of Scientific Discovery) explaining his view that the wave-function description is incomplete:“Should we regard the wave-function whose time dependent changes are, according to Schrödinger equation, deterministic, as a complete description of physical reality, and should we therefore regard the (insufficiently known) interference with the system from without as alone responsible for the fact that our predictions have a merely statistical character?The answer at which we arrive is the wave-function should not be regarded as a complete description of the physical state of the system.We consider a composite system, consisting of the partial systems A and B which interact for a short time only.We assume that we know the wave-function of the composite system before the interaction – a collision of two free particles, for example – has taken place. Then Schrodinger equation will give us the wave-function for the composite system after the interaction.

Assume that now (after the interaction) an optimal measurement is carried out upon the partial system A, which may be done in various ways, however depending on the variables which one wants to measure precisely – for example, the momentum or the position co-ordinate. Quantum mechanics will then give us the wave-function for the partial system B, and it will give us various wave-functions that differ, according to the kind of measurement which we have chosen to carry out upon A.

Now it is unreasonable to assume that the physical state of B may depend upon some measurement carried out upon a system A which by now is separated from B (so that it no longer interacts with B); and this means that the two different wave-functions belong to one and the same physical state of B. Since a complete description of a physical state must necessarily be an unambiguous description (apart from superficialities such as units, choice of the co-ordinates etc.) it is therefore not possible to regard the wave-function as the complete description of the state of the system.”

Anything beyond this in the EPR Phys. Rev. paper is superfluous and irrelevant.In particular there is no reference or wish regarding a possible completion of QM using some classical statistical hidden variables.

4. Bell’s inequalities and theories of correlations

5. Do experimental results indicate (let alone ‘prove’) nonlocality? Entanglement=Nonlocality?!

Beliefs:

1)Experimental results prove that there is nonlocality (violation of Einstein locality)

2)Local Hidden Variable Theories are theoretically valid (no inconsistencies)

From Wikipedia…as a frequent example

Experimentalists such as Aspect used this inequality[1], as well as other formulations of Bell's inequality, to invalidate the hidden variables hypothesis and confirm the existence of nonlocality in quantum mechanics, implying that the lack of determinism in the Copenhagen interpretation was justified.

The case of two ‘spin-half’ particles:

a b

S = 0

A B

1 2 1 2

11 1 1 1

2S

1( , ) : , 1i i i ii

P a b A B A BN

Quantum Mechanics: ( , ) cosP a b a b

Important input

correlation

angle0

-1

1 2( , )QM S sP a b a b a b

( , ) ( , ) ( , ) ( )BellP a b A a h B b h h dh

The essence of Bell’s theorem is that these two correlation functions have distinctly different dependences on the angle between the settings of the apparatus (difference of about 30% at specific angles).

0.25 0.5 0.75 1 1.25 1.5

-1

-0.8

-0.6

-0.4

-0.2

corr

elat

ion

angle

A

A’

B

B’

Consider the quantity ' ' ' 'AB A B A B AB (1,2) ' ' ' ' ( ') '( ')S AB A B A B AB A B B A B B

Now, the assumption ‘reality’ is made

, , ', ' 1A B A B

' (1, 2) 2 '

' (1.2) 2

Either B B S A

Or B B S A

(1,2) (1,2) , 2 (1,2) 2 2P S P P

(1,2) 2 2QMHowever S

So, what does the experimental confirmation of the violation of Bell’s inequality imply as valid theoretical statements that are logically rigorous?

1)Quantum mechanics is validated as a good theory of correlations…

2)A classical hidden variable theory in which statistically distributed valued of the HV determine measurement outcomes is validated as a possible good theory of correlations provided there is violation of Einstein locality.

The common sin is to mix the two and claim that experiments prove nonlocality!

A reanalysis of what Bell did to get the inequalities:

( , ) ( ) ( , ) ( , ), ( ) 1B

P a b h dh A a h B b h h dh

Since ( ) ( ) and ( , ) 1, Bell wrote

( , ) ( ) ( , ) ( , )B

BA a B a P a a

P a b h dh A a h A b h

( , ) ( , ) ( ) [ ( , ) ( , ) ( , ) ( , )]

( ) [ ( , ) ( , ) ( , ) ( , ) ( , ) ( , )]

( ) ( , ) ( , )[ ( , ) ( , ) 1]

B BP a b P a c h dh A a h A b h A a h A c h

h dh A a h A b h A a h A b h A b h A c h

h dh A a h A b h A b h A c h

( , ) ( , ) ( ) [1 ( , ) ( , )] 1 ( , )B B B

P a b P a c h dh A b h B c h P b c

Simultaneous definite values for quantum mechanically non-commuting observables!

Since ( ) ( ) and ( , ) 1, we write

( ( ), ( )) ( ) ( ) ( ) ( ) ( ) ( )!A A

A B A B

A B B A

z z P z z

P x z h dh x z h dh x z

( , ) ( ) ( , ) ( , ), ( ) 1B

P a b h dh A a h B b h h dh

Since ( ) ( ) and ( , ) 1, Bell wrote

( , ) ( ) ( , ) ( , )B

BA a B a P a a

P a b h dh A a h A b h

CSU, Proc. SPIE Photonics 2007

If nonlocal influence are allowed then any classical theory (of the coin tossing type) can be made to reproduce whatever correlations one demands!

Hence the strict logical implication of the experimental results is that a classical theory of the type Bell considered can be a valid theory of microscopic phenomena IF one allows nonlocality as an additional feature.

This then takes away the uniqueness of quantum theory, contrary to the common belief.

1) Correlation functions of quantum mechanics are direct consequence of the CLASSICAL conservation laws arising in space-time symmetries (fundamental conservation laws), applied to ensembles.

2) Any theory that has a correlation function different from the ones in QM is incompatible with the fundamental conservation laws and space-time symmetries, and therefore it is unphysical. Local hidden variable theories fall in this class. Bell’s inequalities can be obeyed (in the general case) only by violating a fundamental conservation law, making them redundant in physics.

3) The origin of Bell’s inequalities can be traced unambiguously to the single step of ignoring wave-particle duality and has nothing to do with the violation of Einstein locality .

4) The logical implication of the experimental result that Bell’s inequalities are violated is that a classical statistical theory can reproduce quantum correlations (or any arbitrary correlation for that matter!) only if it violates Einstein locality, and NOT that QM is nonlocal!

CSU, Europhys. Lett, 2006, Pramana-J.Phys (2006)

6. The belief of the reality of zero-point modes in vacuum

22

4 4

0.013( ) .

240c

cP d dyne cm

d d

d

No long-wavecut-off outside

12 0,1,2,3...n

nn

E n where n

E

Energy of vacuum modes (Casimir Force)

However, this accepted view clashes severely with cosmology

Cosmology:General features that are observationally supported:

• The Universe is expanding at the rate of 2x10-18 m/s/m

• The density of the Universe is about 2x10-29 g/cm3

• There is a background radiation with the black body spectrum at the temperature of 2.728 K

• The Universe is approximately isotropic and homogeneous at very large scales

2

2 8

3

R GH

R

Rate of expansion is proportional to the sqrt. of average density

Energy density of QUANTUM VACUUM

312 0

Energy density

1/ ; c

iAll Modes i

E V h dV

Even with a sharp cut-off in frequency (x-rays…) > 1 g/cm3

But, observations (cosmology, astrophysics): Average cosmic density < 10–29 g/cm3

COSMOLOGICAL CONSTANT PROBLEM

Something is seriously wrong with Quantum Field Theory

7. Black holes and information loss – serious misunderstanding of black hole gravity

2

2:

GMHorizon Surface R

c

The entire problem is formulated with us or asymptotic frames as the observers

Questions:

1.Can we hide information inside a blackhole by throwing it in from far away?

2.Is there information loss?

A very important result from general relativity:

There is exponentially increasing redshift on all processes approaching a black hole horizon by free fall.

Clearly, the observer who is not freely falling with whatever that is falling in will never manage to put anything into the blackhole and will never face the loss of information into the horizon. All free falls towards a blackhole as observable from a frame far away is asymptotic in time and it needs infinite time to reach the event horizon.

Entanglement = Nonlocality

This can be held only by somebody who is sinning hard and confuses quantum description and a classical statistical description of microscopic phenomena. If you describe phenomen involving entnaglement using a classical statistical theory, then you need nonlocality (influence outside the lightcone).