Research Methods Plas lasma School, Pt. Pt. Said (2 (2018 ), , Le - - PowerPoint PPT Presentation

Research Methods

Plas lasma School, Pt.

• Pt. Said (2

(2018), , Le Lecture I I

Amr El-Zant Centre for Theoretical Physics The British University in Egypt

The subject matter

• Two major schemes
• 1- Brief introduction to how physical science and its basic methods work
• 2- Evaluating ideas quantitatively by order of magnitude (1, 10, 100…)
• Hope to
• 1- Convey experience of the language of science and its community
• 2- Convey spirit of critical analysis based on quantitative reasoning
• Warning: presentation necessarily highly idiosyncratic!

(personal in choice of emphasis and topics)

• Illustrates the language but does not teach how to speak

(comes from practice and interaction)

++ Does not include some sociological issues; re collaborations, conferences, funding, career boosting…

To

• Gain ‘Secure’ Knowledge of World
• Just observe  find empirical patterns?
• By logical deduction  thinking hard?
• Actually by a mix of theory and observation/experiment

Use ‘innate’ concept of causality to order flux of observations Order the physical world Form preliminary theory based on observations Test through critical logic and targeted observations/experiments More refined theory

Popperian Knowledge Production

• Comes in two stages: Conjectures and Refutations
• Stage I : propositions  may be born of the irrational
• Stage II: refutations  critical rationalism

 All scientific knowledge contingent  subject to continuous testing  Well tested – logically-empirically – knowledge lasts longer  Forms basis of ever expanding body

Wha hat t it it pr practicall actically mea y means? ns?

• Entering research  entering a tradition

Body of knowledge associated  language, practices, interests, rituals…

• Stages of Initiation  Initial Rites of Passage

1- Know language concepts, relations, mathematical structure 2- Criticise, evaluate logically, empirical, quantitatively 3- Identify active research topics no one interested  may be a good reason! 4- Any ideas you may have must be in language and norms of traditions

The basic body of f knowledge (ill

(illustrates his istoric ical l evolu lutio ion)

• Classical mechanics (the fundamental language of physics is formed)
• Electrodynamics

(extension of language to fields)

• Statistical mechanics (including kinetics, dealing with the complex)
• Quantum Mechanics (logical structure of most fundamental level known)
• High level research in theoretical physics requires background at the level of

the classic series by Landau and Lifshitz (more texts upon request!)

Next xt Step: ‘The Literature’

Once a topic catches interest: 1- Monographs (advanced texts for mature reader with no exercise etc) 2 – Reviews (long papers by established experts outlining development) 3 – Classic papers (seminal articles illustrating development of ideas) 4 – Current papers (a huge flux ~ 50 papers per day on astro alone) 5 – Topical developments (letters, nature articles, press releases etc)

Some Jo Journals

• Reviews of Modern Physics, Physics Reports, Reports on progress in Physics
• Physical Review, Int. Jour. of Mod. Phys.. Journal of Physics, Physica…
• Phys. of Plasma, Jour. Stat. Phys., Phys. of Fluids…
• Astrophys. Jour., Mon. Not. Roy. Ast. Soc.. Astron. & Astrophys.
• Classical and Quantum Grav., Gen. Rel. & Gravitation, jour.Cos. Astropart. Phys.
• Physical review Letters, Physics Letters, Astrophysical Journal Letters etc…

Evaluating the merchandise

• Popperian logic  most of papers wrong or criticizing the wrong!
• Distinguishing takes experience, knowledge and critical mind

** Learn how to read a paper (isolate key claims from intro., abs. conc., figs, eqs.) ** Compare with other work, logic of presentation, clarity, details, reproducibility…)

• Reviews are useful, especially if written by prominent scientists

 but beware of bias and pushing of specific paths! Publication in the most prestigious journal does not mean correct (neither does reputation of authors) But often means that it is ‘wrong enough’ so that its critique provokes serious discussion and interesting ideas  path forward

Evaluating in independently (people will

(people will also also do it to do it to you!)

• u!)
• List what you know
• Does idea for solution contradict (aspects of) what is known?
• What could be important for phenomenon at hand?
• Does proposed solution include these?

Need to know how to Estimate essential contributions  divide problem (to ‘conquer’) Do it quantitatively  learn to calculate! and what to calculate with (basic physical and mathematical ideas!)

Evaluating Own Id Ideas

(to initiate an Investigation)

• Most ideas are wrong  can be shot down simply!
• Most ‘proper’ calculations (or experiments) are difficult and tedious

May take months and involve expensive equipment  produce results that are not easily interpreted  make mistakes and not understand how, where  Perfect methods mentioned in previous slide! Need way to guess feasibility given what is known and sanity check! Communicate basic ideas to community and potential collaborators *** While still keeping quantitative!

HO HOW? W? Order of f Magnitude Calculation (r (rest of f talk lks)

Template f for Quantitative Reasoning and Communication

• The art of estimating given what is known (and thus often predicting the unknown!)
• Isolate essentials, simplify situation -- the spherical cow – understand the essentials exhaustively
• Focusing on what can be solved  progress by iterative refinement

(this is how good science happens in general)

• Master the science of placing constraints
• Apprehend and use conservation laws, scaling, dimension, dimensionless numbers
• - evaluate what is reasonable, makes sense… cross-check results

 Disciplined intuition, imagination born of practice   seriousness and consciousness of assumptions

Estimate Anyt ything: Piano Tuners in Chicago and… ‘Sabakeen’ in Pt. Said!

• E. Fermi (FD stats., Fermi theory of weak int. first nuclear reactor…)
• A mark of a great physicist is the ability to estimate…

1- How many people in Chicago? 3 M 2- How many families? ¾ M 3- How many of them have Pianos? ~ 1/5 4- How many times tuned per year ~ 1 5- How many pianos a tuner can tune per year? 5 * 300 answer ~ 100 Notes on Method: ‘Divide and Rule’ Use of input output – ‘continuity’ relation Sabakeen in pt said ~ 700 000/5 *1 * 1 / (5* 300) ~ 100 Refine up! More than one bath? More than once broken per year ~ few hundreds?

Constraining the Population of f Cairo

• Use structural knowledge. In terms of surface density:

𝑸𝒑𝒒𝑫𝒃𝒋 = ׭

𝑻 𝜯 𝒆𝑩

𝐛𝐨𝐞 𝚻 = ׬

𝟏 𝒊 𝝇 dl

• Cairo made of made of buildings … What’s the density in a building?

Natural units: apartments  ~ few 10’s to few hundred meters contain from 1 – 10 people  ground volume density 𝝇~

𝟐 𝟐𝟏𝟏 𝒖𝒑

𝟏. 𝟐 /𝐧𝟑𝐠𝐦𝐩𝐩𝐬 * f f: ratio of built up areas to roads and greens  f ~ 1 in 3ashwaeat to f < 0.1 in suburbs. h: in floors ~ few to few tens  ‘Typical’ central Cairo 𝜯 ~ 𝟏. 𝟏 𝟔 ∗ 𝟕 ∗ 𝟏. 𝟒

𝒒𝒇𝒔𝒕𝒑𝒐 𝒏𝟑

~ 𝟐𝟏𝟏 𝟏𝟏𝟏 𝒒𝒇𝒔𝒕𝒑𝒐/𝒍𝒏𝟑

• Circumference of Cairo: take ring road at 100 km/s ~ hour. Radius 100/ 2 * 3 km ~ 20 km.  S ~ 1000 km^2
• Constraints population < 100 000 000… also > 1/100 * 4 * 0.1 * 1 000 000 * 1000 = 4 000 000 person
• Can do much better if we discretize integral above into areas : σ𝒋,𝒌 𝝇𝒋 𝜠𝒎 𝜠𝑩𝒋

Egyptian Population Growth

• Continuity equation

ð𝑶 𝝐𝒖 = 𝐆𝐣𝐨 − 𝐆𝐩𝐯𝐮

• Per year flux of babies = number (baby) / couple yr * number (couples)
• Couples ~ adult population/2 ~ 100 Million/4 ~ 25 Million
• Married for ~ 35 years, will get n children
• F (in) ~ 25 M /35 * n
• F (out) ~ 100 M /70

𝑮𝒋𝒐 𝑮𝒑𝒗𝒖 ~ 𝟖𝟏 𝟒𝟔 ∗ 𝟑𝟔 𝟐𝟏𝟏 ∗ 𝒐 = 𝟏. . 𝟔 ∗ 𝒐

 equilibrium at n = 2 , n= 4 gives

𝑮𝒋𝒐 𝑮𝒑𝒗𝒖 = 𝟑



𝑮𝒋𝒐 𝑮𝒑𝒗𝒖 − 𝟐 = 𝟐  𝑮𝒋𝒐−𝑮𝒑𝒗𝒖 𝑼𝒑𝒖𝒃𝒎

=

𝟐 𝟖𝟏 ~ 𝟐. 𝟓 %

** Actual value around 2 % and n = 3.3 … which numbers you think need modification?

Distances to astronomical objects

• Again: What do we know?
• Moon must be light seconds away (remember Apollo communication?)

Moon is about half a degree in angular size

• Eye resolves less 1/30 of that
• But all planets seem like points in sky

If ~ size (moon) > ~ light minute away But they are resolved with modest telescopes  ~ light hrs away Sun: Eight minutes away, also about half degree on sky Stars: distant suns, cannot be seen with most high resolution telescopes  must be further than 30 * 8 * (100*60) ~ 1400000 minutes > 2.7 light yrs  need very high res as in VLT ++

How many stars in diffuse galactic disk?

• There are about 10 000 scattered stars ~ light year away
• Make up ~ same light of disk stars
• Diffuse band cannot be resolved by eye or measured by earth based parallax

 > Few * 100 light years away ++ since light luminosity decreases as 1/𝑒2  nearby stars contribute most  Distance to most contributing stars ~ 1000 light years Million times less luminous/ per star ~ similar apparent brightness to scattered stars  Disk contains 10 000 000 000 stars   𝟐𝟏𝟓 ∗ 𝟐𝟏𝟒 𝟑 = 𝟐𝟏𝟐𝟏 (𝒈𝒑𝒗𝒔 + 𝒕𝒋𝒚 𝒑𝒔𝒆𝒇𝒔𝒕)

Of judicious simplifying assumptions: An Ancient Miracle

Eratosthenes (director, Alex lib.): 1- Sun rays parallel 2- Earth: sphere 

In many ways similar to our current understanding of universe! Got answer right to 1 % (what does that mean?)

Some homework…

• A car trunk is found filled with bags of Egyptian bills; estimate how much money can

be in it, placing physical constraints on the maximum amount.

• If the maximum possible height of a mountain is set by the downward force that the

rocks at its base can withstand, and Mt Everest the maximum height mountains for

• n Earth, estimate the maximum possible height of mountains on Mars relative to

mount Everest

• The first Egyptian deep space probe has mass of 1000 tonnes, including 30

astronauts and 100 tonnes of foul and mekhallel. Its nuclear reactor has total energy

• utput of 1000 J. This energy will be used to accelerate 40 tonnes of Helium

backward thrust. How long would it take to arrive to Proxima Centaury… would there be enough foul left when they arrive.?

• How many house light bulbs can run on a car engineconnected to electricity

generator?

The Moral… and More

• Science can ask ‘deep’ questions, but is not about knowing why there is something rather than nothing
• It is about quantitatively, securely knowing something rather than nothing
• Simple curiosity  conjectures  tests  refinement and refutation  better conjectures that logically

correspond to the world

• Science  language and linguistic community, with norms and rituals.

These include quantitative discussions based on simple estimates. They are tools of communication

• Enter through basic background  literature  own research (then conferences workshops, collaborations…)
• Initiating interesting research again requires intuition based on familiarity with laws and methods

Ability to estimate  quantitatively, quickly evaluate, constrain and dismiss conjectures  refutation, refinement… by researcher, collaborators and community * Coming talk: Estimating size of white dwarf, neutron stars & BH event horizons; formation of galaxies and more..