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EXAMS Summer 2023 > P&R Block 1 > Flashcards

P&R Block 1 Flashcards

1
Q

What was the “paradox” raised by Saint Augustine?

A

The present is all that can be said to truly exist, but the present only exists for an instant.
The moment associated with the present turns into the past instantaneously.

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2
Q

What is “temporal reductionism”?
Who is this associated with?

A

Aristotle and Leibniz.

All temporal statements can be reduced to statements about temporal relations between events.

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3
Q

What is “absolutism with respect to time”?
Who is this associated with?

A

Plato and Newton.

There is some “true time”, independent of events. Time is like a container in which events are placed. Time exists in the absence of events.

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4
Q

Who is the idea of “time series’” associated with?

A

McTaggart

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5
Q

What are the A and B-series?

What was the supposed conclusion of these arguments?

A

A-series: events are ordered past, present, future. (“real change”)

B-series: events are ordered from earlier to later and are independent from the “present”.

Conclusion: time is “not real”.

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6
Q

What is a “presentist” view?

What about “block universe” and “growing block universe”?

A

Presentist: only the present is real.

Block universe: all times and events are real, we experience movement through the 4D block universe.

Growing block universe: the past and present are equally real, but the future is not real.

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7
Q

What kind of laws are time-reversible?
Why are they sometimes not? Why is this not an issue?

A

Microscopic ones

CP asymmetric weak interactions must also be time-asymmetric. However, there is no proposed connection between this asymmetry and the “arrow of time”.

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8
Q

What is the name of the precursor to the entropic argument for the thermodynamic arrow of time?

A

Boltzmann’s H-theorem (1872)

A function H that is non-increasing in time.

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9
Q

What is the stasszahlansatz, and why was this an issue with Boltzmann’s H-theorem?

A

The molecular chaos hypothesis.

i.e. Boltzmann assumed particle velocities and positions are uncorrelated. However, correlations do build up over time due to collisions, and by ignoring this, Boltzmann introduced time-asymmetry.

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10
Q

What is poincare recurrence?

A

Certain closed systems will return to a state arbitrarily close to their initial state given sufficient time.

However, this is usually not a valid argument against the thermodynamic arrow of time, as the required sufficient time may be arbitrarily large.

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11
Q

How is Boltzmann entropy defined?

A

S_B = k ln(Omega)

k is the Boltzmann constant.
Omega is the volume of phase space corresponding to the macrostate M(X). Where X is the associated microstate.

  • minus sign is missing in the phase-space definition as opposed to the probability definition
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12
Q

How can the argument that Boltzmann entropy always increases be simply stated?

A

Higher entropy states are associated with an exponentially larger phase space volume.

It is overwhelmingly likely for a system to evolve to a microstate associated with a higher entropy macrostate.

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13
Q

What is the “past hypothesis”?

A

The arrow of time is a result of the universe being in a very low-entropy state at the “beginning”.

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14
Q

Who (and when) can the term “arrow of time” be attributed to?

What was this “arrow of time” referring to?

A

Eddington (1928)

His arrow of time was the thermodynamic one: time’s arrow points in the direction of increasing entropy of a system.

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15
Q

How many different “arrows of time” can you name?

A

Thermodynamic
Cosmological
Causal? / Psychological
Radiative
Quantum

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16
Q

Who wrote the paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”?

When?

A

Eugene Wigner, 1960

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17
Q

What does Joel Lebowitz (1993) believe about the arrows of time?

A

All arrows of time are the result of the initial low-entropy state of the universe.

A “measurement” formalism in QM can have a second-law-type time-asymmetric component, such that the quantum arrow of time can be traced to the initial low-entropy state of the universe.

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18
Q

What is the formula for Shannon information?
What is the theoretical basis of this generalisation?

A

I(p_i) = - log_2( p_i )

The generalisation of the concept of how many binary questions are required to determine which state (with associated p_i) a system is in.

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19
Q

What is the formula for Shannon Entropy?
What can this quantity be thought of?
Why is it called Entropy?

A

= - sum( p_i * log_2[p_i] )

The average information generated by a system: the weighted average of the information given by each state. Can be thought of as an “average surprise” function.

Has the same form as Gibbs entropy (the generalisation of Boltzmann entropy). [as pointed out by Von Neumann]

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20
Q

What is the unit of entropy?

A

Joules per Kelvin (sometimes also per kg)

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21
Q

Who first formally made the connection between information theory and statistical physics?

What is a key result relating to this connection?

A

Jaynes (1957)

The Boltzmann distribution can be obtained from Shannon entropy with the constraint of energy conservation, using Lagrange multipliers.

22
Q

What is Maxwell’s demon?

A

1870
Classic demon powers (knows the positions and momenta of all elements of a system).
In this case, the demon reduces the entropy of a system without doing any work, by opening and closing a door separating two chambers.

23
Q

What is the Szilard engine?

A

(1929)
A development of Maxwell’s demon, into an engine that does not require a demon.
Heat is converted into work with 100% efficiency, as long as the position of a particle in a box is known.
This violates the Kelvin-Planck statement of the second law.

24
Q

How was the issue of Maxwell’s demon (or the Szilard engine) resolved?

A

(1929) Szilard suggests entropy increase must be associated with measurement.
(1951) Brillouin suggests energy is required to make a measurement.
(1961) Landauer proposes the LANDAUER PRINCIPLE: information is physical.
(1982) Bennet argues that it is the ERASURE of this physical information that leads to entropy increase.

25
Q

What is the Landauer Principle?

A

Information is physical, information must be physically stored.
The erasure of ONE BIT leads to entropy increase of at least k ln(2).

26
Q

What is stochastic thermodynamics?

A

The study of small thermodynamic systems.
Small thermodynamic systems have energy scales comparable to k T (the energy scale of fluctuations).

27
Q

What is a large thermodynamic system?
What is an example of a small thermodynamic system?

A

Large thermodynamic systems have ~an Avogadro number of molecules, and fluctuations about equilibrium cannot be resolved.

Molecular processes in biological systems are examples of small thermodynamic systems.

28
Q

What modification of the second law is required in order for it to apply to stochastic thermodynamics?

A

The PROBABILITY of entropy increasing is always greater than the probability of entropy decreasing.

i.e: there are trajectories for the state of a small system in which entropy decreases over a small time period.

29
Q

What is a resolution of the “issue” that the second law is expressed as an inequality while all other fundamental physical laws are expressed as equalities?

A

The Jarzynski relation is an expression of the second law that uses an equality.

30
Q

What is Bayes theorem?

A

P(A given B) = P(B given A) * P(A) / P(B)

31
Q

What is the take-home message of Rudolf Peierls’ “Irreversibility” (1979)?

A

Thermodynamic behaviour is NOT asymmetric in time.

Given a low entropy state, time can be projected in either direction. Our inability to observe the reverse direction is due to the necessary involvement of a scientist to set up “initial” conditions.

For a small thermodynamic system, low entropy states can manifest spontaneously, in which case both “forward” and “backward” trajectories are realised.

32
Q

How does Feynman rephrase the second law?
What thought experiment does he use to demonstrate the impossibility of a reversible engine?

A

“The availability of energy is always decreasing”

The “Ratchet and Pawl” is decribed.

33
Q

What kind of systems do not produce entropy increase?

A

Systems in equilibrium.

34
Q

What is Laplace’s Demon?

A

Classic demon (knows all positions and momenta) can predict the future in a completely deterministic universe.

35
Q

Which paper kick-started the field of non-linear dynamics and complexity?

A

Lorenz - Deterministic Nonperiodic Flow (1962)

*Lorenz attractor

36
Q

How is Chaos characterised?

A

Extreme sensitivity to initial conditions - exponential divergence (“butterfly effect”).
i.e: positive Liapunov exponents.

Requires non-linearity, but not all non-linear processes are chaotic. Simple, deterministic systems can be chaotic.

37
Q

What is the “Logistic map” an example of?

A

A simple, discrete time system that exhibits chaos.

x_[n+1] = rx_[n] (1 - x_[n])

38
Q

What is the difference between methodological reductionism and theory reductionism?

A

Methodological reductionism is a research strategy: the best way to understand the properties of an entity is via entities that constitute it.

Theory reductionism is the idea that a more fundamental theory can be used to derive less fundamental results/theories.

39
Q

Who is an example of a proponent of reductionism?
What is a key point made?

A

Weinberg
“arrows of scientific explanation seem to always point to the level of the very small, and eventually maybe a theory of everything”

Feynman?

40
Q

Who are some examples of people who make the case against reductionism?
Give some key contributions.

A

Anderson (“More is different” - biology is not just applied chemistry).
Mayr (advances in microworld understanding will not impact understanding of middle world).
Goldenfeld and Kadanoff (“Don’t model bulldozers with quarks”).

41
Q

What is emergence?

A

A property arising from the components of a system acting together, not obviously traceable to the properties of the interacting components.

42
Q

What does Anderson mean by: “The reductionist hypothesis does not imply a constructionist one”?

A

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.

43
Q

What properties are usually associated with “complex” systems?

A

Sensitivity to initial conditions.
Non-linear.
Emergent properties.
Lots of interacting components.

44
Q

What is an example of the failure of the reductionist approach, from genetics?

A

Humans and worms have ~ the same number of genes, the hypothesis of a 1:1 relationship between genetic complexity and organism complexity is refuted. There must be some complex non-linear behaviour.

45
Q

What is the “mesoscopic world”?

A

The scale between the microscopic and the macroscopic.
e.g: molecular biological processes.

46
Q

What are 7 reasons for modelling?
*Give some names also (2)

A

Mostly from Epstein (Why Model?):

  • Models allow explaining as well as predicting.
  • Models inform which data should be collected.
  • Models can be applied to novel situations, not possible with a data-only approach.
  • Sensitivity of predictions to changes in modelling parameters can be evaluated.
  • New questions are raised.
  • Suggests analogies between different dynamical systems.
  • (Frigg) Useful as an educational/explorative tool, e.g. phi^4 model in QCD allows exploration of renormalisation and symmetry-breaking.
47
Q

What is the difference between an implicit model and an explicit model?

A

Implicit modelling is a process that happens constantly during human thought.

Explicit modelling is based on assumptions that are acknowledged. Explicit models are replicable.

48
Q

What is a phenomenological model?

A

A model that is not based on underlying theory, but purely attempts to reproduce experimental results.

49
Q

What are some examples of Galilean idealisation?

A

Point masses, frictionless surfaces, isolated systems…

50
Q

What is the argument being made in: Anderson - the end of theory?

A

The idea that exploitation of big data removes the need for models. Computers can be simply provided with data and asked to find patterns/correlations.

51
Q

What are arguments against Anderson’s paper - “the end of theory”?

A
  • Science is not about finding patterns, it is about finding explanations for those patterns.
  • The collection of data must be informed by scientific theory. Otherwise, the results are strongly dependent on the factors resulting in the kind of data that is collected. (this can result in bias due to social/economic/political factors).
  • Data by themselves are meaningless. They must be interpreted in the framework of some model or theory.
  • Heisenberg: “We have to remember that what we observe is not nature in itself, but nature exposed to our method of questioning”
52
Q

What is the name of the guy that believes that all arrows of time are reducible to the “past hypothesis”?

A

Lebowitz

EXAMS Summer 2023 (6 decks)

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