1

New Theories / What is non-returning twin paradox?

« on: 17/09/2023 08:30:13 »

This is a slightly modified twin paradox to distinguish the effects of relative speeds and acceleration.
Twin A started a journey to Alpha Centauri 4 light years away in a space ship moving at 0.4c. He is expected to arrive 10 years later, according to earth observer.
Twin B stayed home to improve the space ship, so he can go to Alpha Centauri 5 years later at 0.8 c.
Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously. Does special theory of relativity predict the same?
How old are they when they meet up at Alpha Centauri?

2

Science Experiments / How many types of capacitance are there?

« on: 15/09/2023 05:26:25 »

Wikipedia distinguishes capacitance into two different types, i.e. self capacitance and mutual capacitance.
https://en.wikipedia.org/wiki/Capacitance

Capacitance is the capability of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance.[1]: 237?238  An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.

The capacitance between two conductors is a function only of the geometry; the opposing surface area of the conductors and the distance between them, and the permittivity of any dielectric material between them. For many dielectric materials, the permittivity, and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.

The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates.[2] The reciprocal of capacitance is called elastance.

Are they mutually exclusive to each other, without overlap?
Are there any other types of electric capacitance beside them?

3

Just Chat! / What's your advice on writing a series of story?

« on: 05/08/2023 15:45:20 »

For years, I've been plotting a long story following a main character growing up from childhood into adulthood. It has something similar to Harry Potter series. For Asian kids, perhaps Naruto is more familiar to them. Older kids may be more familiar with Dragon Ball or Kungfu Boy. They are extremely popular among children, and some adults too. There's something we can learn from them.

Unlike those examples, the genre of my story is science fiction, and the goal is to introduce and socialize /popularize critical thinking, science literacy, and basic ethics to children so they could be equipped with mental tools to face the world in front of them.

My plot also covered the main characters in adulthood, where their decisions have higher stake and affect many people's lives.

4

Science Experiments / How do electromagnetic couplings work?

« on: 21/05/2023 22:18:39 »

Let's Experiment with an Electromagnetic Chain!

Have you ever seen an electromagnetic chain? Its a series of electric and magnetic toroid  cores linked in the form of a chain transferring power from electricity to magnetism and back again as it works it way along the device. Its a great hands-on illustration of Maxwell's equations as well as an illustration of transformer action taken to extremes.

5

Science Experiments / What phenomena can be demonstrated by a cheap high voltage generator?

« on: 27/03/2023 16:39:27 »

I've got one of it, and recorded some videos with it. It can generate spark 1 to 2 cm long in open air. Some dielectric barrier can prevent the formation of spark. I think there are many interesting things can be shown with it.

6

Science Experiments / How to build DIY lasers?

« on: 24/12/2022 10:31:11 »

I just found a great Youtube channel named Les' Lab, explaining how to build DIY laser. I'd like to share the videos here. I hope you find them useful.

Nitrogen Laser tear down, power up, and Home Made Dye Laser Demonstration

7

Technology / How to learn process control system in practice?

« on: 16/11/2022 13:39:57 »

We were just finished a project commissioning and starting up a new process plant. One of the most frequently asked questions during this phase, which came from production operators, shift leaders, interns, as well as engineers from other fields, is how to tune parameters of PID controllers. But it is just the tip of an iceberg. To do it properly, we need to understand the fundamental basics first.

I summarized them in my videos. Here's the first one, splitting a system into a process model and control model. The splitting concept was very useful when I need to build a simulation of a process control system to let users get first-hand experience in tuning a PID control without causing upset in real process. It lets users see for themselves how a system response to disturbances as well as changes in PID parameters.

8

Physics, Astronomy & Cosmology / How much precession is observed in Parker Solar Probe's orbit?

« on: 15/09/2022 15:17:51 »

Parker Solar Probe's orbital period is similar to Mercury's. But the eccentricity is significantly different. How does it affect its precession?

https://en.wikipedia.org/wiki/Parker_Solar_Probe
Semi-major axis   0.388 AU (58.0 million km; 36.1 million mi)
Perihelion altitude   0.046 AU (6.9 million km; 4.3 million mi; 9.86 R☉)[note 1]
Aphelion altitude   0.73 AU (109 million km; 68 million mi)[5]
Inclination   3.4°
Period   88 days

https://en.wikipedia.org/wiki/Mercury_(planet)
Aphelion   0.466697 AU;  69,816,900 km
Perihelion   0.307499 AU;  46,001,200 km
Semi-major axis   0.387098 AU;  57,909,050 km
Eccentricity   0.205630[3]
Orbital period (sidereal)   87.9691 d;  0.240846 yr

The perihelion precession of Mercury is 5,600 arcseconds (1.5556°) per century relative to Earth, or 574.10±0.65 arcseconds per century[132] relative to the inertial ICRF.

9

Science Experiments / How to demonstrate polarization of light?

« on: 26/08/2022 11:07:09 »

Polarization of electromagnetic wave can be easily demonstrated using microwave and radio wave due to the macroscopic size of their wavelengths and the antennae. In this thread I'll show how to demonstrate the phenomenon using light.

Investigation on Polarization of Light 1 : Brewster's Angle

Demonstration of  polarization of light using reflection by dielectric material.

10

New Theories / What makes Riemann's Hypothesis Hard to Prove?

« on: 27/06/2022 15:40:12 »

What makes Riemann's Hypothesis Hard to Prove?
First, an introduction.

https://en.wikipedia.org/wiki/Riemann_hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
1/2
. Many consider it to be the most important unsolved problem in pure mathematics.[1] It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is named.

The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.

The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ(s) = 0 when s is one of −2, −4, −6, .... These are called its trivial zeros. The zeta function is also zero for other values of s, which are called nontrivial zeros. The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that:

The real part of every nontrivial zero of the Riemann zeta function is
1/2
.

Thus, if the hypothesis is correct, all the nontrivial zeros lie on the critical line consisting of the complex numbers
1/2 + i t, where t is a real number and i is the imaginary unit.

You may find the visualization in this video to be helpful.

Visualizing the Riemann zeta function and analytic continuation

11

New Theories / Can black hole be electrically charged?

« on: 28/05/2022 06:08:22 »

If electrons are continuously shot into a black hole (from beta radiation or electron gun), will it be electrically charged?
Can the charge be sensed from outside, i.e. the Coulomb force?
How does the black hole mass affect the strength of Coulomb force, by modifying the distance from an outside object?

12

Science Experiments / How does induction heater work?

« on: 30/03/2022 11:40:06 »

How does induction heater work? This video can provide a starting point for us to understand the device better.

In this video I will show you how a common induction heater works, what kind of materials it can heat up and how you can easily create your own.

I've got a cheap ZVS (zero voltage switch) induction heater to explore its behavior. It has 120W maximum power, and working at 5-12VDC. I've tested its functionality, and I'm planning to investigate further on its characteristics, and how it reacts to different things.

13

Science Experiments / How does microwave superheat water?

« on: 16/03/2022 13:52:07 »

I just found old raw videos I took while discussing in this thread.
https://www.thenakedscientists.com/forum/index.php?topic=78517

I guess it's time to edit and upload them, so the information that they contain becomes available to more people.

14

Science Experiments / What's electro-magneto hydro dynamics?

« on: 08/02/2022 09:07:28 »

This experiment is about Magnetohydrodynamics

While this experiment is about Electrohydrodynamics

I think to myself, why not combine those effects in the same experiment?

15

Physiology & Medicine / What's the most practical method to detect sleep deprivation?

« on: 16/01/2022 15:02:55 »

This article reminds me of some incidents on the road and industrial work place caused by sleep deprivation of the driver or machine operator, which could have been prevented.
https://neurosciencenews.com/sleep-deprivation-serotonin-2a-19897/
Is there a practical method to detect cognitive decline caused by sleep deprivation or intoxication? Perhaps something like blood pressure, heart rate, or brain wave detector? Non-invasive methods would be preferred. And the result should be available within few minutes.

16

Physics, Astronomy & Cosmology / How can we see ultraviolet light in Balmer series?

« on: 28/12/2021 11:24:30 »

https://en.wikipedia.org/wiki/Balmer_series

The "visible" hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right. Four lines (counting from the right) are formally in the visible range. Lines five and six can be seen with the naked eye, but are considered to be ultraviolet as they have wavelengths less than 400 nm.

How can we see ultraviolet light in Balmer series?

17

Just Chat! / Can we be sure of our own existence

« on: 13/11/2021 06:39:04 »

If you add enough "necessary axioms", you can end up believing whatever made them necessary. Hence religion, a flat earth supported on turtles, and other kinds of foolishness.

Better to start with observations.

The only thing we can be sure of is our own existence.  Any other things can be deceiving, including our observations.
An assumption is necessary if it can somehow be related to our existence.

18

General Science / What's 0^0 ?

« on: 02/11/2021 03:16:16 »

What's 0 to the power of 0?

19

New Theories / How Many Numbers Exist?

« on: 29/09/2021 04:53:12 »

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

There are an infinite number of infinities. Which one corresponds to the real numbers?

An Infinity of Infinities
Yes, infinity comes in many sizes. In 1873, the German mathematician Georg Cantor shook math to the core when he discovered that the “real” numbers that fill the number line — most with never-ending digits, like 3.14159… — outnumber “natural” numbers like 1, 2 and 3, even though there are infinitely many of both.

Infinite sets of numbers mess with our intuition about size, so as a warmup, compare the natural numbers {1, 2, 3, …} with the odd numbers {1, 3, 5, …}. You might think the first set is bigger, since only half its elements appear in the second set. Cantor realized, though, that the elements of the two sets can be put in a one-to-one correspondence. You can pair off the first elements of each set (1 and 1), then pair off their second elements (2 and 3), then their third (3 and 5), and so on forever, covering all elements of both sets. In this sense, the two infinite sets have the same size, or what Cantor called “cardinality.” He designated their size with the cardinal number ₀ (“aleph-zero”).

But Cantor discovered that natural numbers can’t be put into one-to-one correspondence with the continuum of real numbers. For instance, try to pair 1 with 1.00000… and 2 with 1.00001…, and you’ll have skipped over infinitely many real numbers (like 1.000000001…). You can’t possibly count them all; their cardinality is greater than that of the natural numbers.


Sizes of infinity don’t stop there. Cantor discovered that any infinite set’s power set — the set of all subsets of its elements — has larger cardinality than it does. Every power set itself has a power set, so that cardinal numbers form an infinitely tall tower of infinities.

Standing at the foot of this forbidding edifice, Cantor focused on the first couple of floors. He managed to prove that the set formed from different ways of ordering natural numbers (from smallest to largest, for example, or with all odd numbers first) has cardinality ₁, one level up from the natural numbers. Moreover, each of these “order types” encodes a real number.

His continuum hypothesis asserts that this is exactly the size of the continuum — that there are precisely ₁ real numbers. In other words, the cardinality of the continuum immediately follow ₀, the cardinality of the natural numbers, with no sizes of infinity in between.

But to Cantor’s immense distress, he couldn’t prove it.

In 1900, the mathematician David Hilbert put the continuum hypothesis first on his famous list of 23 math problems to solve in the 20th century. Hilbert was enthralled by the nascent mathematics of infinity — “Cantor’s paradise,” as he called it — and the continuum hypothesis seemed like its lowest-hanging fruit.

To the contrary, shocking revelations last century turned Cantor’s question into a deep epistemological conundrum.

The trouble arose in 1931, when the Austrian-born logician Kurt Gödel discovered that any set of axioms that you might posit as a foundation for mathematics will inevitably be incomplete. There will always be questions that your list of ground rules can’t settle, true mathematical facts that they can’t prove.

As Gödel suspected right away, the continuum hypothesis is such a case: a problem that’s independent of the standard axioms of mathematics.

These axioms, 10 in all, are known as ZFC (for “Zermelo-Fraenkel axioms with the axiom of choice”), and they undergird almost all of modern math. The axioms describe basic properties of collections of objects, or sets. Since virtually everything mathematical can be built out of sets (the empty set {} denotes 0, for instance; {{}} denotes 1; {{},{{}}} denotes 2, and so on), the rules of sets suffice for constructing proofs throughout math.

In 1940, Gödel showed that you can’t use the ZFC axioms to disprove the continuum hypothesis. Then in 1963, the American mathematician Paul Cohen showed the opposite —you can’t use them to prove it, either. Cohen’s proof, together with Gödel’s, means the continuum hypothesis is independent of the ZFC axioms; they can have it either way.

https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/

What do you think about this continuum hypothesis?

20

New Theories / Is there a better way to explain light?

« on: 12/07/2021 02:12:39 »

This thread is a follow up of my previous thread discussing and criticizing existing theories about light.
https://www.thenakedscientists.com/forum/index.php?topic=68595.0

Here I'll try to figure out if there is a way to improve it. If there is, what will it look like?

I just become aware that a similar topic has been created by CrazyScientist.
https://www.thenakedscientists.com/forum/index.php?topic=82373.0
What Is The Nature Of Photons & EM Radiation?

He has his own reasoning to come to his conclusion, which has some differences and similarities than my current understanding of this matter. If I have something to say about his reasoning, I'll post it there. But to avoid complication, I'll post my own reasoning here.

To avoid getting unexpected results, I'll try to avoid making false assumptions, especially the hidden ones, which are likely hard to identify. Any assumptions put into the model should be stated explicitly, along with the reasons why they can't be dismissed. This can significantly slow down the process, but I guess it worths the efforts to resolve spookiness in science.