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What does Quantum Mechanicstell us about the universe?

Mark Alford

Washington UniversitySaint Louis, USA

More properly: What do experiments tell us about the universe?

1

What the experts say

“I think it is safe to say that no one understands quantum

mechanics.” (Richard Feynman)

“Anyone who is not shocked by quantum theory has not

understood a single word.” (Niels Bohr)

2

Dr. A. Einstein on Quantum Mechanics

“God is subtle, but he is not malicious.” (1921)

“God does not play dice.” (1926)

“This theory reminds me a little of the system of

delusions of an exceedingly intelligent paranoiac,

concocted of incoherent elements of thoughts.”

(1952)

3

Suggested Reading:

• “The Infamous Boundary” (David Wick)

• “Is the moon there when nobody looks?”

(David Mermin, Physics Today April 1985).

4

What does quantum mechanics allow us to understand?

Everything that happens at small distances.

• Structure and behavior of atoms

• Chemistry

• Stability of matter

• Behavior of light (interference, photons. . .)

• Behavior of matter (conductivity, superconductivity, heat

capacity. . .)

• Electronics

• Subatomic constituents of matter (particle physics)

• Radioactivity

• Antimatter

• · · ·

So what’s the problem?

5

What’s weird about quantum mechanics?

Classical physics

Newton - 1920 : Universe described by deterministic laws of physics.

Deterministic means the results of all possible measurements are (in

principle) predictable and encoded in the state of the system.

Probabilistic statements are only necessary when we don’t know everything

about a system.

Quantum mechanics

1920 - now : quantum mechanics is highly successful, but gives predictions

only in terms of probabilities.

Executive Summary

• The universe seems to be inherently probabilistic.

• There cannot be a deeper deterministic theory∗.

Nature doesn’t know what result you’ll get until you do the measurement.∗(unless you allow faster-than-light travel in the deeper theory).

6

Schrodinger’s Cat

In QM, the state of a radioactive atom

is a mixture (“superposition”) of being

intact and having decayed. Over time,

the “intact” part shrinks to zero and

the “decayed” part rises to 100%.

This may be OK for atoms, but we can

put the atom near a Geiger counter,

and when it detects the decay it sets

off a poison spray, which kills a cat.

After 10 mins, suppose the atom is in a 50/50 state of being intact/decayed.

So if we open the box, there is a 50/50 chance the cat will be alive/dead.

But before we open the box? QM says the cat is in a 50/50 mixture. . .!?

7

Precursors to quantum mechanics

1900-1905: Planck and Einstein:

Quantization of energy of electromagnetic

field (photons) to explain thermal radiation

and the photoelectric effect.

1913: Bohr: “Bohr atom”; like a little solar

system, but with quantization of energy levels.

Explains simple atomic spectra.

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The early stages

1913-1923: Bohr atom cannot explain quantized spin of electron,

spectra of large atoms, response to magnetic fields, etc.

1923: Heisenberg and Born∗:

Matrix mechanics.

Heisenberg: “It is my genuine conviction that an interpretation. . . in terms

of circular and elliptical orbits of classical geometry has not the least physical

meaning.”

∗: Grandfather of Olivia Newton-John

9

Invention of quantum mechanics

1926: Schrodinger and Born: Wave mechanics.

• The “wavefunction” tells you the probability of

finding the electron in different places.

• Schrodinger’s equation tells you how the wave-

function evolves in time.

• Mathematically equivalent to Heisenberg’s Matrix Mechanics.

10

Schrodinger: life of a physicist

1887 born in Vienna.

1920 married Annemarie (“Anny”) Bertel.

1921 became professor at Univ of Zurich, became close friend of Weyl.

1925 formulated quantum mechanics (aged 38!) during Christmas vacation at an Alpine

resort with “an old girlfriend from Vienna”, while Anny stayed home in Zurich.

1927 became professor in Berlin.

1933 sought a position at Oxford for himself and a colleague, Arthur March. Schrodinger had

had several affairs and was now in love with Arthur March’s wife Hilde. Anny had

already taken Schrodinger’s friend Weyl as her lover for many years.

1933 moved to Oxford, accompanied by Anny, Arthur and Hilde. Received Nobel Prize.

1934 Hilde gives birth in Oxford to Schrodinger’s child.

1934 offered permanent position at Princeton, but offer fell through because he wanted to

live at Princeton with Anny and Hilde both sharing the upbringing of his daughter.

1936 moved to Graz, Austria.

1938 after the Anschluss, dismissed from his post by the Nazis.

1939-56 moved to Dublin. Had two more daughters while in Dublin, by two different Irish

women.

1956 returned to Vienna.

1961 died of tuberculosis.

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Schrodinger and Heisenberg:

proud parents of quantum theory

The wave function is easy to visualize, and evolves deterministically

according to Schrodinger’s equation.

But when we make physical predictions, the wave function only tells us

the relative probabilities of different outcomes (Heisenberg’s

uncertainty principle).

Schrodinger: “My theory was inspired by de Broglie and. . . Einstein. No

genetic relationship whatever with Heisenberg is known to me. I knew of his

theory, but felt discouraged, not to say repelled, by the methods. . . and by

the lack of visualizability.”

Heisenberg: “The more I reflect on the physical portion of Schrodinger’s

theory, the more disgusting I find it. . . What Schrodinger writes on the

visualizability of his theory. . . I consider trash.”

12

Accepting the weirdness: the Bohr-Einstein debates

1927-1930 Einstein tries to show

that even within quantum mechanics,

sufficiently clever measurements can

avoid the uncertainty principle.

Bohr refutes every attempt.

Conclusion:

Within quantum mechanics, Heisenberg’s uncertainty principle cannot

be evaded. QM predictions are inherently probabilistic.

But probabilities are usually just a sign that we don’t know everything.

Are the probabilities in QM predictions like that?

Could there be a deeper deterministic theory that would tell us which

outcome we will observe? (“hidden variables”). No.

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The ultimate weirdness: no underlying determinism!

How do we know the universe is fundamentally vague (probabilistic)?

Why couldn’t there be an underlying deterministic theory?

(1) Einstein-Podolsky-Rosen/Bohm (“EPR”) thought-experiment:

brings the probabilistic nature of QM to the surface.

(2) “Bell Inequality” : Deterministic theories only allow a limited set

of outcomes of EPR experiments: they obey Bell’s inequality

(3) Perform EPR experiments : results violate Bell’s inequality and

agree with QM’s probabilistic predictions.

Conclusion:

No deterministic theory can reproduce QM.

(unless the deterministic theory allows faster-than-light travel)

Experimental results agree with QM: reality is probabilistic.

14

The EPR/Bohm experiment

1 2 1 2

source

1

2

• Source produces “spin-zero” pairs of particles, with opposite spins

• Each detector has a 3-way switch: red, green, blue.

• The detector sends the particle either to a + slit or a − slit.

We set detector 1 to ask, Is your spin pointing in the red direction?”, particle says “No” (−).

We set detector 2 to ask, “Is your spin pointing in the green direction?”, particle says “Yes” (+).

15

How an EPR-type experiment would behavein a deterministic universe (Bell Inequality)

p(1: ),2:

)

)

,2:

,2:

1

+ p(1:

+ p(1:

12::

12::

12::

12::

12::

12::

12::

12::

Select asubset

States of thesystem

12::

12::

12::

12::

12::12::12::12::

Bell Inequality:prob(subset) 1

In QM, by contrast, the outcomes of the measurements are not already encoded in

the state of the system: they aren’t “decided” until the measurement occurs.

16

Quantum mechanics predicts violation of Bell Inequality

Deterministic system

p(1 : , 2: )

+ p(1 : , 2: )

+ p(1 : , 2: )

6 1

Quantum mechanics

p(1 : , 2: ) = 3/8

p(1 : , 2: ) = 3/8

p(1 : , 2: ) = 3/8

total: 9/8 = 1.125

Conclusion:

When you measure the particle spins in an EPR experiment, the

answer you get cannot be encoded in the state of the system.

Nature doesn’t know what the result will be

until you make the measurement.

17

Experimental observations agree with QM

Nature 403,

pp 515 - 519

(03 Feb 2000)

18

Conclusions about quantum mechanics and the universe

• QM describes the world with fabulous accuracy.

• QM somehow manages to be both

– deterministic: the evolution of the wavefunction

– probabilistic: predictions of measurement results

• The probabilistic vagueness seems to be a feature of nature.

• We still don’t have a clear picture of what a quantum-mechanical

universe is like: is it one world with collapsing wavefunctions

(Copenhagen) or Many Worlds, or something else?

19

Science and philosophy

Science does not provide a suitable foundation for metaphysical

speculation, i.e. deep eternal truths about the world.

Experiments produce unexpected results.

Theories change.

19th century: stable universe, obeying deterministic classical laws.

20th century: expanding universe of finite age, obeying probabilistic

quantum-mechanical laws.

Who knows what will come next?

20

The universe does not have to be understandable, let alone easily

understandable. As we learn more, our theories become weirder. . .

“My own suspicion is that the universe

is not only queerer than we suppose, but

queerer than we can suppose.”

(J.B.S Haldane, 1927)

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