CULTURAL QA 09202417
SCIENCE QA –BASE QUORA QA, Compiled
Q1 Did Einstein make any mistakes in the derivation of his special
relativity theory despite being known as a genius?
KR I It is not narrated well in the answer.
Albert Einstein, one of the most celebrated physicists of all time, did
indeed make errors in his work, as is the case with many scientists. The
process of scientific discovery often involves trial and error, revision,
and refinement. Here's a brief overview of how Einstein addressed errors in
his derivations and how he corrected them:
Early Work and Errors: In his early work, particularly his theories of
relativity, Einstein initially made some mistakes or faced challenges in
deriving equations. For instance, in his 1905 paper on special relativity,
he made a conceptual error regarding the invariance of the speed of light
in different reference frames. He had to refine his ideas to ensure that
they were consistent with experimental evidence and the theory's internal
logic.
Cosmological Constant: One of the most famous examples of Einstein's errors
was his introduction of the cosmological constant (Λ) {LAMDA} into his
equations of general relativity. When Einstein first published his field
equations in 1915, they did not account for a static universe, which was
the prevailing belief at the time. To reconcile his equations with the
assumption of a static universe, he added the cosmological constant. Later,
when the expansion of the universe was discovered by Edwin Hubble, Einstein
discarded the constant, calling it his "biggest blunder." However, the
cosmological constant has since found a new role in modern cosmology,
related to dark energy and the accelerated expansion of the universe.
Quantum Mechanics and the Einstein-Podolsky-Rosen (EPR) Paradox: Einstein
was skeptical of quantum mechanics, particularly the notion of entanglement
and the probabilistic nature of quantum states. In the 1935 EPR paper,
Einstein, along with Podolsky and Rosen, proposed a paradox to question the
completeness of quantum mechanics. Although this paradox highlighted
important issues in quantum theory and led to further debate and research,
the development of quantum mechanics and experimental tests (such as Bell’s
theorem) have largely confirmed the theory’s predictions, although some
interpretations continue to be debated.
Refinements and Corrections: Throughout his career, Einstein was open to
revising his theories based on new evidence and peer feedback. The
scientific method requires that theories be continually tested and refined.
Einstein’s willingness to acknowledge and correct his errors was a key part
of his scientific process. For example, he revisited and refined his work
on general relativity multiple times as new data and insights emerged.
Einstein’s experience underscores a fundamental aspect of science: the
ability to learn from mistakes and continually refine theories in light of
new evidence. His legacy is not only in his groundbreaking theories but
also in his approach to scientific inquiry, which values rigor, openness,
and the pursuit of truth.
II A few examples of other scientists who made well-known errors:
Isaac Newton: Newton made errors in his early work on optics and the nature
of light. For example, his initial theory of color based on prisms was
incomplete and did not fully account for the wave nature of light. It was
later refined by scientists like Thomas Young and Augustin-Jean Fresnel.
Newton also struggled with his theories of gravitation and motion, and his
calculations sometimes led to inaccuracies that were later corrected by
other scientists.
Niels Bohr: Bohr’s early model of the atom, the Bohr model, was
groundbreaking but eventually proved incomplete. It worked well for
hydrogen but struggled with more complex atoms. The development of quantum
mechanics by physicists like Werner Heisenberg and Erwin Schrödinger
provided a more accurate description of atomic behavior.
Linus Pauling: Pauling was a brilliant chemist, but he made a significant
error in his work on the structure of DNA. He initially proposed a triple
helix structure for DNA, which was incorrect. The correct double helix
model was later proposed by James Watson and Francis Crick, with crucial
contributions from Rosalind Franklin.
Fred Hoyle: Hoyle was a strong advocate of the steady-state theory of the
universe, which posited that the universe had no beginning or end and was
constantly creating matter. The discovery of the cosmic microwave
background radiation and the acceptance of the Big Bang theory showed that
Hoyle’s steady-state theory was incorrect. Despite this, Hoyle made
substantial contributions to nucleosynthesis and stellar evolution.
Lamarck: Jean-Baptiste Lamarck proposed an early theory of evolution that
included the idea of inheritance of acquired characteristics (e.g., that
giraffes have long necks because their ancestors stretched them). This idea
was later refuted by Charles Darwin’s theory of natural selection and
modern genetics. However, Lamarck’s work was important in the history of
evolutionary biology.
Aristotle: While not a modern scientist, Aristotle made many incorrect
scientific claims, particularly in his observations of biology and physics.
For instance, he believed in the idea of spontaneous generation (that life
could arise from non-living matter). These ideas were later challenged and
corrected by scientists such as Louis Pasteur.
III Einstein's famous equation 𝐸=𝑚𝑐2
E=mc2 is widely regarded as one of the most accurate and well-established
results in physics. This equation, which relates energy (𝐸 E) to mass (𝑚m)
with 𝑐c representing the speed of light in a vacuum, was derived as part
of Einstein's theory of relativity. It fundamentally describes the
equivalence of mass and energy and has been confirmed by numerous
experiments and observations.
However, like any scientific theory or equation, its application and
understanding can have nuances:
Contextual Accuracy: The equation 𝐸=𝑚𝑐2
E=mc 2 applies to scenarios where mass is converted entirely into energy,
such as in nuclear reactions. In more complex systems or in the context of
general relativity, where gravitational effects and varying reference
frames come into play, additional factors might be involved. For instance,
in high-energy particle physics or cosmology, corrections and additional
factors come into play, but the fundamental equation remains a cornerstone.
Experimental Verification: The predictions derived from 𝐸=𝑚𝑐2
E=mc2 have been experimentally verified in numerous ways, such
as in particle accelerators where particles are accelerated to high speeds
and their energy and mass are measured. The success of this equation in
predicting experimental results underlines its robustness.
Limitations and Extensions: While 𝐸=𝑚𝑐2E=mc2 is accurate in the realm
of special relativity, general relativity and quantum field theory extend
our understanding of how mass and energy interact under different
conditions. For example, in quantum mechanics, energy and mass are often
treated within frameworks that consider quantum effects, but 𝐸=𝑚𝑐2 E=mc
2 remains a key principle.
Misinterpretations: Sometimes, the equation is misunderstood or misapplied
outside its proper context. For instance, in practical scenarios involving
chemical reactions, the mass-energy conversion is incredibly small compared
to nuclear reactions, so 𝐸=𝑚𝑐2 E=mc 2 is not usually significant in
those contexts.
In summary, 𝐸=𝑚𝑐2 E=mc 2 is not considered to have errors in its
derivation or application within its appropriate domain. It remains a
central result of modern physics with extensive experimental validation.
However, like all scientific principles, its applicability is
context-specific, and understanding its limitations and scope is crucial
for accurate application.
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Q2 Why, if you put two liquids with different densities, the one with
the bigger density goes down?
KR: SCIENTIFIC EXPLANATION: ” Density is a measure of how much
mass is contained in a given volume. It is a fundamental concept in both
physics and chemistry and can be described mathematically as:
Density(𝜌)=Mass(𝑚) / Volume(𝑉) Density(ρ)= Volume(V) / Mass(m)where:𝜌 ρ
(rho) is the density, 𝑚 m is the mass of the substance, 𝑉 V is the volume
it occupies.
Key Points About Density:
Units: The units of density depend on the units of mass and volume used.
Common units include:
Kilograms per cubic meter (kg/m³): SI unit
Grams per cubic centimeter (g/cm³): Often used in chemistry and everyday
contexts
Pounds per cubic foot (lb/ft³): Common in the U.S. customary system
Physical Interpretation:
High Density: A substance with high density has a lot of mass packed into a
small volume. For example, lead is very dense compared to aluminum.
Low Density: A substance with low density has less mass per unit volume.
For example, air has a much lower density than water.
Density and Buoyancy: Density plays a crucial role in buoyancy. An object
will float in a fluid if its density is less than the density of the fluid.
Conversely, it will sink if its density is greater.
Temperature and Density: Density can change with temperature because most
substances expand when heated (increasing volume) and contract when cooled
(decreasing volume). This temperature dependence must be considered in
precise measurements and applications.
Density of States: In physics, particularly in statistical mechanics and
solid-state physics, the term "density of states" refers to the number of
available quantum states at a specific energy level.
Example Calculations:
Water: The density of water at 4°C is approximately 1 g/cm³ or 1000 kg/m³.
This means that 1 cubic centimeter of water has a mass of 1 gram, and 1
cubic meter of water has a mass of 1000 kilograms.
Lead: The density of lead is about 11.34 g/cm³. So, a cubic centimeter of
lead weighs 11.34 grams.
Understanding density is crucial for various applications, including
material science, engineering, fluid dynamics, and everyday tasks such as
cooking and shipping.
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Q3 How does an object's volume change when it expands?
KR: SCIENTIFIC EXPLANATION: Volume and expansion are related
concepts that describe how the size of an object or substance changes in
response to various conditions, typically temperature or pressure. Here's a
detailed look at both concepts:
Volume
Volume is the amount of space that a substance or object occupies. It is a
three-dimensional measurement and can be calculated for various shapes and
substances. The standard unit of volume in the International System of
Units (SI) is the cubic meter (m³), but other units such as liters (L) and
cubic centimeters (cm³) are also commonly used.
Common Volume Formulas:
Cube: 𝑉=𝑎3V=a 3 (where 𝑎a is the length of a side)Rectangular Prism:
𝑉=𝑙×𝑤×ℎV=l×w×h (where 𝑙l is length, w is width, and ℎh is height)
Sphere: 𝑉=43𝜋𝑟3
V= 34 πr 3 (where 𝑟r is the radius)
Cylinder: 𝑉=𝜋𝑟2H ℎV=πr 2 h (where 𝑟r is the radius and ℎh is the
height)
Expansion
Expansion refers to the increase in volume of a substance due to changes in
temperature, pressure, or other conditions. There are several types of
expansion:
Thermal Expansion: Most materials expand when heated and contract when
cooled. This is due to the increase in kinetic energy of the atoms or
molecules, which causes them to move apart.
Linear Expansion: For solids, linear expansion describes how the length of
an object changes with temperature. The formula is:
Δ𝐿=𝐿0⋅𝛼⋅Δ𝑇ΔL=L 0 ⋅α⋅ΔT
where:Δ𝐿
ΔL is the change in length, 𝐿 0 L 0 is the original length,
𝛼 α is the coefficient of linear expansion, Δ 𝑇
ΔT is the change in temperature.
Volume Expansion: For liquids and gases, volume expansion describes how the
volume changes with temperature. The formula is:
Δ 𝑉 = 𝑉 0⋅𝛽⋅
Δ𝑇 ΔV=V 0 ⋅β⋅ΔT
where:Δ𝑉ΔV is the change in volume,
𝑉0V 0 is the original volume,
𝛽β is the coefficient of volumetric expansion,
Δ𝑇ΔT is the change in temperature.
Pressure-Volume Relationship: In gases, volume can also change with
pressure according to Boyle’s Law, which states that the volume of a gas is
inversely proportional to its pressure at constant temperature:
𝑃1𝑉1=𝑃2𝑉2 P 1 V 1 =P 2 V 2 where:
𝑃1 P 1 and 𝑉1 V 1 are the initial pressure and volume,
𝑃2P 2 and 𝑉2V 2 are the final pressure and volume.
Thermal Expansion in Solids, Liquids, and Gases:
Solids: Solids expand primarily in length (linear expansion) and volume
(volumetric expansion).
Liquids: Liquids generally expand more than solids for the same temperature
change. This expansion can affect buoyancy and density.
Gases: Gases expand significantly with temperature and pressure changes, as
described by the ideal gas law:
𝑃𝑉=𝑛𝑅𝑇
PV=nRT
where:𝑃P is the pressure,𝑉V is the volume,𝑛n is the number of moles of
gas,𝑅R is the gas constant,𝑇T is the temperature in Kelvin.
Applications and Considerations
Engineering and Construction: Understanding thermal expansion is critical
in designing structures and materials that can withstand temperature
changes without warping or cracking.
Manufacturing: Volume changes due to temperature need to be accounted for
in processes like casting and machining.
Meteorology: Atmospheric pressure and temperature affect the volume of
gases, which influences weather patterns and climate.
Everyday Life: Common occurrences, like the expansion of metal lids in hot
water or the contraction of a balloon in cold air, illustrate thermal
expansion principles.
Understanding how volume and expansion interact helps in various
scientific, engineering, and practical contexts, ensuring systems function
correctly under varying conditions.
K Rajaram IRS 17924
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---------- Forwarded message ---------
From: 'gopala krishnan' via iyer123 <[email protected]>
Date: Tue, 17 Sept 2024 at 19:29
Subject: [iyer123] Cultural QA 09-2024-17
To: Iyer <[email protected]>
CULTURAL QA 09-2024-17
SCIENCE QA –BASE QUORA QA, Compiled
Q1 Did Einstein make any mistakes in the derivation of his special
relativity theory despite being known as a genius?
A1 Bert Willke, Ph.D. in Physics, Massachusetts Institute of
Technology (Graduated 1963) Sep 11
Yes. There are at least 2 mistakes in the famous 1905 paper in which
Einstein created what he later called special relativity.
In that 1905 paper Einstein set out to prove that if the speed of light is
invariant; then relative spatial and temporal coordinates between any 2
things moving with constant relative velocity are given by the Lorentz
transformations. A couple of statements early in his 1905 attempt apply
only in Galilean relativity, making his 1905 attempt self-contradictory.
Einstein corrected his mistake in 1907 with a much simpler derivation free
of contradictions. Einstein was still just a humble Swiss patent office
clerk in 1907 whose reputation was not yet established, so he might be
forgiven for not endangering his new special relativity by acknowledging a
mistake in that seminal 1905 paper. So far as I know, he never did
acknowledge that mistake even after his reputation became firmly established
.
Near the end of Einstein’s 1905 relativity paper Einstein attempted and
failed to extend special relativity to encompass acceleration. Planck
offered a more plausible setting for acceleration in special relativity in
1906, and Einstein patched Planck’s result ad hoc into his renewed attempt,
in the same 1907 paper in which he correctly derived the L.T.’s, to
establish acceleration in special relativity. The matter wasn’t resolved
until, after an 8 year struggle, Einstein succeeded in incorporating
acceleration into relativity in 1915 with his new general relativity. So
far as I know, Einstein and Planck never officially withdrew their failed
1905, 1906, and 1907 attempts to bring acceleration into special relativity.
A few people are still using Planck’s 1906 model since it’s much simpler
than Einstein’s 1915 tensor model. However Einstein’s 1915 general
relativity seems to be correct, at least so far; and Planck’s 1906 idea
doesn’t share that distinction. Special relativity is solely about things
moving with constant relative velocity, and questions involving
acceleration must be handed over to general relativity.
Q2 Why, if you put two liquids with different densities, the one with
the bigger density goes down?
A2 Silk Road, Physics/History Connoisseur, AI Machine Learning.12h
Say we have two ships.One's a sleek yacht, the other's a chunky cargo
vessel.
They're both in the same harbour, but the yacht sits high on the water,
while the cargo ship sinks low.
Why?
Same reason a denser liquid sinks below a less dense one - it's all about
weight and space.
Imagine each liquid is made of these tiny particles.
Denser liquids have more of these particles packed into the same space.
It's like comparing a box full of feathers to a box full of rocks. The
rocks are denser, so that box is heavier.
Gravity's always pulling everything downwards.The heavier something is, the
harder gravity pulls.
When you mix two liquids, the denser one, with its greater weight, gets
pulled down more strongly.
The less dense liquid, meanwhile, is sort of pushed out of the way.
Like the yacht getting nudged aside as the cargo ship settles in.
This doesn't mean the less dense liquid is "weak" or anything, it's just
lighter, so gravity's grip on it isn't as strong.
This whole process happens until the denser liquid is at the bottom, and
the less dense one is on top.
They find a balance, a state of equilibrium where gravity's pull on each
liquid is countered by the upward push from the liquid below it.
This principle is everywhere in nature.
Oil floats on water, cream rises to the top of milk.
Q3 How does an object's volume change when it expands?
A3 Daniel Iyamuremye, Former Senior Lecturer (Retired) (2000–2018) ·
9m
When an object expands, its volume increases
Q4 Why do professional biologists say that humans are the ape
counterpart to the axolotl?
A4 David M. Prus, Lifelong interest in animal behavior, ecology, and
evolution Aug 13
It’s called Neoteny.
Neoteny is the retention of juvenile characteristics
So while an axolotl looks like a baby of another salamander, and only
develops into an adult morph if fed certain hormonal chemicals.
Humans look like baby apes
Baby apes have proportionately bigger, rounder heads and flatter faces,
shorter body hair, longer head hair, small brow ridges, small nose and
teeth, While a human adult retains the flat face and round cranium.
Neoteny in Humans
Patterns of Neoteny in the relative skull growth in Homo and Pan Succesive
stages of skull development from infancy to maturity in chimpanzees (top
three) and humans (bottom pair). Infants of both species have a large
craniums and small faces. Relatively more rapid growth of the jaw in
juvenile chimps (above, middle) gives them skull proportions resembling
those of adult humans, in which the relative proportions are less altered
(right). Continued rapid expansion of the jaw in adult apes (top right &
below right) gives them proportionately larger jaws and smaller crania. The
two photographs of a juvenile and adult male chimpanzee are from a 1926
study by the German anthropologist Adolf Naef. Of the former, he says," [It]
is the most human-like picture of an animal, of any that is known to me ."
It’s possible this is why those features are appealing to people, and how
our ancestors stood out, all while allowing for a greater brain capacity
thanks to our giant baby heads. The cost is weaker teeth and jaws and FAR
more difficult, long and dangerous pregnancy and delivery.
Q5 Why do coconut trees leave at only the top of their stems?
A5 Dudla Jyothi, M Sc (Ph D) in Life (biological) & Genetics and Heredity,
Mt. Carmel High School (Graduated 1981)Sep 1
It is because of how they grow. Single trunk palms cannot branch, and grow
only from their top, the single growing point. This is sometimes called a
crown shaft, at the top of the trunk. Cut that off, the tree dies. The
whole leaf is called coconut fond. stalk (petiole) of frond = Midrib. then
leaflet of a frond.
Cocoanut trees have something called sclerenchyma fibers present in their
trunks. It is a type of plant tissue which grows vertically and does not
allow the coconut trees to branch out, resulting in Coconut trees grow in
height.
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