# Imponderables

From Derek

Collecting "imponderables" or interesting unanswered questions is one of my hobbies and I list a bunch of questions here. I decided to put them on this web site to encourage students to think creatively and identify deep questions. But anyone is welcome to enjoy them. I know the answer to some of them, and I have posted them in case others come up with an answer more elegant than I know. However, many are open questions to have fun with. Maybe some can never be answered. The questions are also here to encourage interdisciplinary thinking.

For ease of updating and ease of interaction, I've decided to post all my questions on ResearchGate.

## Contents

## Physics questions

- Why are Galilean and Lorentz transformations not equivalent at low speeds?
- How to explain the diffraction pattern through a net curtain?
- Is it possible to find a temperature in the universe lower than the cosmic background?
- When do we use conservation of momentum vs. conservation of energy?
- Just before sunset, does your shadow move with infinite velocity?
- To what extent is thermal noise a result of the quantum world?
- Can anyone explain tacking against the wind?
- Is "left and right" fundamental in physics or arbitrary?
- Does creation of the universe violate physical law?
- Are there any aspects of physics that are inviolate and absolutely immutable?
- Is gravitational field a fiction?
- What is the weight of information?
- How many bits of information can be contained by the whole universe?
- Where does mgh potential energy reside exactly?
- Which physical variables do not exist in conjugate pairs and do not have an uncertainty relationship in quantum mechanics? Can you list which pairs exist, and list those variables that don't exist in pairs?
- Is it possible to weigh yourself only using an iPhone?
- Is there a thought experiment that demonstrates if virtual particles are real?
- Which physical variables are allowed a quantum superposition and what is it they all have in common?
- What is the nature of a vacuum that causes its permittivity to be non-zero?
- Can you explain what happens when you photocopy a mirror?
- If a demon ate the whole universe what would its temperature rise be?
- How do we know when to add quantities in quadrature?
- Are there limits to the size of the single-photon double-slit experiment?
- Is the time a single photon source emits indeterminate?
- Why does kinetic energy transfer between colliding objects?
- Is it possible to distinguish thermal bodies in equilibrium?
- Why does Planck's black-body equation only account for polarization modes? Why not OAM?
- Can you explain why a yacht can go faster than the wind driving it?
- Where does the energy go in a Mach-Zehnder interferometer?
- Can Einstein's principle of equivalence be violated near a black hole?
- Why doesn't the colour of light appear to change when you pass it through a chopper?
- What would happen to the universe if there were no vacuum fluctuations?
- How do we know if our physical variables form a minimum set?
- Explain how a wine glass resonates at a wavelength bigger than the glass
- Why does resolution depend on wavelength?
- How many uncertainty relationships are there?
- Is energy conserved for moving observers?
- Does accelerated charge emit photons to all observers?
- Can the one-way speed of light be measured using entangled photons?

## Math questions

- What is the probability of finding a point on a plane?
- Can you solve the necktie paradox?
- Can the digits of pi be used as a random seed to generate itself?
- Can information asymmetry be exploited for receiver authentication?
- Is Cauchy-Riemann a necessary or sufficient condition?
- Why does the formula for the Nth digit of pi have to be in base 16?
- What is the number system that would obey a quantum version of Erdos-Kac?
- The paradox of infinity: where does the nonlinearity come from?
- Is there a solution to the paradox of taking limits to zero for z = x^y ?

## Biology questions

- Are humans the only species that go through menopause?
- Why don't humans have a baculum?
- Is there any known anticorrelation between cancer and autoimmunity?
- What do high levels of Strontium 88 in human hair mean?
- Is there any evidence that paternal mtDNA can be transmitted to one's offspring?
- Are there any organisms that don't get cancer?

## Botany questions

## Computer science questions

- Is computation possible without any stable states?
- What are the basic ingredients for computation, and what extra ingredient is needed to make life?
- How do you access web indexing for a customized search engine?

## Electrical & electronic engineering questions

- If an electrical isolator has a resistor connected to one port and another resistor at the other, does one resistor get hotter?
- Does a cell phone transmission penetrate a microwave oven?
- Why are there no practical applications of negative impedance?
- Is it possible to cheat and create a room temperature superconductor that exploits an external power source? Would that have useful applications?
- Are wavelengths cut off in the quasistatic regime of the wave equation?
- What happens when you drive a moving plate capacitor with noise?
- Do the number of electromagnetic modes in a coax cable depend on its length?
- Why do TEM modes have no low-frequency cut-off?

## Philosophy questions

- Is mathematics a human contrivance or is it innate to nature?
- Are there any mathematics for which there is absolutely no application in physics?
- Are there any types of human experiments for which ethics committee approval is generally not needed?
- Using a series of thoughts can the human brain generate a random number in an unbiased way?
- What measure of confidence can be put into a long mathematical proof?
- Without
*a priori*information, is it possible to tell the difference between a human language, a machine language, and a biological coding language?