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The models, theories, and laws we devise sometimes imply the existence of objects or phenomena that are as yet unobserved. These predictions are remarkable triumphs and tributes to the power of science. It is the underlying order in the universe that enables scientists to make such spectacular predictions. However, if experimentation does not verify our predictions, then the theory or law is wrong, no matter how elegant or convenient it is. Laws can never be known with absolute certainty because it is impossible to perform every imaginable experiment to confirm a law for every possible scenario. Physicists operate under the assumption that all scientific laws and theories are valid until a counterexample is observed. If a good-quality, verifiable experiment contradicts a well-established law or theory, then the law or theory must be modified or overthrown completely.
The study of science in general, and physics in particular, is an adventure much like the exploration of an uncharted ocean. Discoveries are made; models, theories, and laws are formulated; and the beauty of the physical universe is made more sublime for the insights gained.
What is physics?
Physics is the science concerned with describing the interactions of energy, matter, space, and time to uncover the fundamental mechanisms that underlie every phenomenon.
Some have described physics as a “search for simplicity.” Explain why this might be an appropriate description.
If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?
No, neither of these two theories is more valid than the other. Experimentation is the ultimate decider. If experimental evidence does not suggest one theory over the other, then both are equally valid. A given physicist might prefer one theory over another on the grounds that one seems more simple, more natural, or more beautiful than the other, but that physicist would quickly acknowledge that he or she cannot say the other theory is invalid. Rather, he or she would be honest about the fact that more experimental evidence is needed to determine which theory is a better description of nature.
What determines the validity of a theory?
Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?
Probably not. As the saying goes, “Extraordinary claims require extraordinary evidence.”
Can the validity of a model be limited or must it be universally valid? How does this compare with the required validity of a theory or a law?
Find the order of magnitude of the following physical quantities. (a) The mass of Earth’s atmosphere: $5.1\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{18}\text{kg;}$ (b) The mass of the Moon’s atmosphere: 25,000 kg; (c) The mass of Earth’s hydrosphere: $1.4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{21}\text{kg;}$ (d) The mass of Earth: $5.97\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{24}\text{kg;}$ (e) The mass of the Moon: $7.34\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{22}\text{kg;}$ (f) The Earth–Moon distance (semimajor axis): $3.84\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{8}\text{m;}$ (g) The mean Earth–Sun distance: $1.5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{11}\text{m;}$ (h) The equatorial radius of Earth: $6.38\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{6}\text{m;}$ (i) The mass of an electron: $9.11\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-31}}\text{kg;}$ (j) The mass of a proton: $1.67\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-27}}\text{kg;}$ (k) The mass of the Sun: $1.99\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{30}\text{kg.}$
Use the orders of magnitude you found in the previous problem to answer the following questions to within an order of magnitude. (a) How many electrons would it take to equal the mass of a proton? (b) How many Earths would it take to equal the mass of the Sun? (c) How many Earth–Moon distances would it take to cover the distance from Earth to the Sun? (d) How many Moon atmospheres would it take to equal the mass of Earth’s atmosphere? (e) How many moons would it take to equal the mass of Earth? (f) How many protons would it take to equal the mass of the Sun?
a. 10 ^{3} ; b. 10 ^{5} ; c. 10 ^{2} ; d. 10 ^{15} ; e. 10 ^{2} ; f. 10 ^{57}
For the remaining questions, you need to use [link] to obtain the necessary orders of magnitude of lengths, masses, and times.
Roughly how many heartbeats are there in a lifetime?
A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?
10 ^{2} generations
Roughly how many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human?
Calculate the approximate number of atoms in a bacterium. Assume the average mass of an atom in the bacterium is 10 times the mass of a proton.
10 ^{11} atoms
(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is 10 times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?
Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?
10 ^{3} nerve impulses/s
About how many floating-point operations can a supercomputer perform each year?
Roughly how many floating-point operations can a supercomputer perform in a human lifetime?
10 ^{26} floating-point operations per human lifetime
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