Graphing tachyons, energy-momentum graph, imaginary mass

*Continuation of the previous two posts introducing tachyons and deriving the energy-momentum relationship

Again, sorry for the pictures but putting in equations on blogger is a futile task

Going to continue to try to figure out the spacelike timelike stuff eventually.....

Thanks again for reading

Derivation of Einstein's Energy, Mass and Momentum Relationship

Sorry for the long delay. I wanted to make my math not be unreadable and hence made the entire post on a google doc and took screenshots. The post, therefore, looks kinda unaligned. 

Do make sure to read the Lorenz factor derivation done in my previous post as this post starts off assuming that you know what the Lorenz factor, γ,  means and that you know what relativistic time/mass mean.

Hope this helps, I'll finally be getting into the astrophysics side of this (tachyons/ energy-momentum/ space-time graphs/ spacelike timelike as soon as I manage to figure that stuff out).

Thanks for reading!

Mehul

Relativity - Deriving the Lorentz Factor

γ or the Lorentz Factor is defined as “the factor by which time, length, and relativistic mass change for an object while that object is moving.” Hence in order to find this constant, let’s define a relationship between time and the relativistic time:

T'=t*(constant)

Where T’ is the relativistic time and t is the time taken. Therefore there must be some constant which is multiplied
to t to get T’. For practicalities sake, let’s define this random constant as γ. Hence:

T'=tγ

Now let’s do some basic geometry:

In the above figure, we can assume for à source emitting a photon at speed c, the distance travelled is simply
c * the time the photon travels for. This makes sense as the distance à photon would travel over five seconds
would simply be (Sorry for the terrible way the equations are written):

5*c=5*3*10^8=1.5*10^9m

At the same time, we can assume that the source s is travelling horizontally at à velocity v which is à fraction
of the velocity c. We however also know that for an observer O, the time will be relative compared to t (T’ = tγ).
Hence we can deduce that the horizontal distance travelled by the source s is vT’.

As the source is moving however, the observer O observes the path of the photon to be:

The problem however now is that the observed distance travelled by the photon is greater than the actual
distance. Hence, as c is à constant, the only way the photon could have travelled à greater distance is if it
has travelled over à greater period of time and hence we multiply the speed of the photon c to the dilated
time T’ (as dilated time for all bradyons is greater to actual time) to get the observed distance travelled by
the photon.

Using more basic geometry, we know using pythagoras’ theorem that:

(cT')^2 = (ct)^2 + (vT')^2

c^2*t^2 = v^2*T'^2 - c^2*T'^2

c^2*t^2 = T'^2 (v^2 - c^2)

On dividing both sides by c2T'2,we get:

t^2 / T'^2 = (c^2 - v^2) / c^2

On square rooting both sides we get:

                            t / T' = sqrroot (1 - v^2 / c^2)                    Eq - 4

As we have previously defined - T'=tγ

Therefore T'/t=γ and hence we have to reciprocate Eq - 4 to get:

    T' / t = sqrroot (1 / 1-v^2 / c^2) = γ                

Hence above is a very simple method of derivation. Again, quick apologies for the messy difficult to read math.

Nuclear Fusion Inside Stars / Fission (Nuclear bombs)

Stars are dense, highly pressurized and extremely hot objects. In these extreme environments, plasma is formed (a state of matter after 'gas') where all the particles get 'unbound' in a way and merge into a singular chargeless fluid.

In this chargeless fluid, as all the particles are unbound and zip around at extremely high speeds, hence many nuclei collide and combine to make a new heavier element. This process releases an extenuatingly large amount of energy. The process was used to make the H-Bomb (many times more powerful than the A-bomb released on Hiroshima and Nagasaki). Essentially nuclei in a plasma state combine and create new nuclei and hence new elements and this process releases energy.

Hence in stars, due to the large amounts of pressure and heat at the cores, nuclear fusion takes place which creates new elements. Our sun in fact constantly fuses hydrogen into helium. However what's really fascinating is the fact that fusion stops at iron. There is a 'binding energy' that is needed to fuse nuclei and iron actually has the greatest binding energy despite not having the greatest molar mass. Hence fusing beyond iron is impossible.

Now moving onto nuclear fission. As some of you may know, isotopes decay through alpha, beta, and gamma radiation and do this based on their half-life. Technitium-99 a common medical isotope decays and has a half-life of 6 hours (extremely short). Alpha and beta radiation both cause a change in the element while gamma does not affect the original element. (Beta decay releases an electron and alpha decay releases a helium nucleus). Hence some scientists started thinking about atoms splitting into constituent elements aka nuclear fission. 

What basically happens is that uranium 235 or plutonium 239 are hit with a neutron beam or with a neutron. The new isotope now undergoes the process of fission and splits into two separate atoms. At this point, three more neutrons are released. If the uranium was in a pile then the new neutrons would irrigate the other uranium and a chain reaction would begin. Each 'fission' of uranium would release 2.5MJ of energy which is well.... a lot. A ton of this uranium would release that much more energy. Hence this chain reaction is what is used in the A-bomb as the large amount of energy/radiation causes the explosion and after-effects.

The missing antimatter problem

Some of you may have heard of the "missing antimatter problem" and in this post, I want to go into detail on what it is and what it means.

Starting off, currently there is way more matter than antimatter. Most things ranging from our books to large stellar bodies all consist of matter while there is very less antimatter. However, the big bang should have released an equal amount of matter and antimatter. Hence scientists are trying to find out the cause of this disparity.



To give a brief overview of what antimatter is, antimatter particles share the same mass as matter particles however they have opposite charges ie. a positive positron (antielectron) is simply the opposite of a negatively charged electron. When matter and antimatter come into contact, they both immediately annihilate and release energy usually in the form of gamma rays



Scientists recently were able to create and analyze an antihydrogen to a significant degree of precision and what's truly fascinating is the lack of difference between the two ie. both the hydrogen atom and the antihydrogen atom had no significant differences.

Currently, there is no explanation for this disparity however one theory has gained some traction. Due to the near infinite volume of the universe, we barely know anything about it. Hence it's not a stretch to say just like matter has formed galaxies, there also might be antimatter galaxies somewhere far in the universe. This is only speculation though as there is no real proof or alternatives.



I'll make sure to keep updating if something interesting is found.

Until then,
Adieu

How we discovered that the universe is expanding

To understand the acceleration of the expansion of the universe, we first have to understand what redshifting is and to understand redshifting we have to understand some basic information about the wave-particle duality of light.

As most physics students know, light has wave and particle-like characteristics and hence has a wavelength and frequency. In simple terms, scientists measure the light from a 1a supernova. However, due to the universe expanding, the light redshifts and scientists can calculate the redshift to figure out the expansion of the universe.

The idea of redshift is based on the fact that if light is attempting to reach somewhere, but the place is moving away at an extremely fast pace. Then light's wavelength increases and hence the colour turns red (visible light spectrum)




Hence while observing light from distant stars, scientists observed that the light was undergoing 'red shifting' and found out that the red shifting was increasing at an accelerated rate and hence the only way for this to happen is if space and hence the universe were to be expanding.

Now that we've gone through the how, let's go through the why. Currently this expansion of the universe is considered to be there due to 'dark energy' which is well...... we don't know. What we do know however is that something is causing this expansion and we have hence coined this something as dark energy. The existence of dark energy and expansion of the universe have led to some scenarios of the future of the universe but I'll go through that in another blog post.

Signing out,
Mehul.

White Holes / Kerr Black Holes / Multiverse Penrose theory Presentation

Hi guys,

Below is a link to my presentation on white holes/Kerr black holes/multiverse Penrose theory.

You can use this for whatever.

https://drive.google.com/file/d/1T7-OoMVPr3QkDWAFh5P0Ql9vcoRhzCgz/view?usp=sharing

Thanks guys,
Mehul

White Holes

Everyone knows of Black hole but most things in the universe have an opposite like matter and anti matter, therefore what is the opposite of something that sucks in everything including light. The answer is a white hole. White holes are very interesting for everyone as it is something that is difficult to imagine. What could be the function of the opposite of a black hole, this is what I'm here to tell you about.

A white hole is a hypothetical region of space time which cannot be entered from the outside although matter and light can escape from it. This must be difficult to imagine. If matter and light cannot enter then how can anything exit as for there to be an exit there must first be an entry. This question is what scientists are trying to answer and their success has been rather limited. Recently in fact some scientists suggested that the Big Bang might have been one massive white hole however due to the fact that the universe is expanding and our lack of knowledge of white holes, this theory has not gained momentum.

A white hole would attract objects just like anything else due to gravity but the objects would never actually reach the center and would keep losing momentum and would need more energy to accelerate. However eventually the amount of energy needed to accelerate past the resistance would be infinite and that number cannot be reached.

Finally my thoughts, I consider white holes to be interesting yet as there is no significant data I'll have to hold on before I put my thoughts down. If a significant discovery is found then I'll be sure to re-post about this topic.

This is Mehul

Signing Out

Space Elevator - the Future of Space Travel?

Some space fanatics might know this idea first proposed by Konstantin Tsiolkosky at 1895. He proposed the idea of a tower reaching geosynchronous orbit. However to make such an elevator we would need a material that is both lighter and stronger than anything we have right now. However the developments with nanotechnologies have allowed for new materials to be created such as Carbon Nanotubes which might just be strong and light enough.


To the right is a diagram showing the system recently proposed. The climber is the elevator with the idea of centrifugal force used to keep the space elevator stable.

The benefit of having a Space Elevator is quite simple. Spaceships launched at that height would already be in space and therefore would not have to escape earth's gravitational field. Due to this they would have more fuel and would not slow down as they would be in a vacuum.

The main reason why the building of this hasnt even started is again simply the price. Due to carbon nanotubes being a new technology, it is quite expensive and to build something on a magnitude of a space elevator would literally cost an unimaginable amount therefore for now there is not enough support but I honestly see this happening quite soon.

In fact, a Japanese company actually plans to have it built by 2050. Obayashi Corp has quite the inspiring goal to have it built soon and I wish them all the luck in succeeding.

Below is another picture detailing the concept behind it. May we all one day be able to take an elevator to space.

This is Mehul, Signing out.

Antimatter

My first post in a long time (Sorry Guys). Today, I will be talking about antimatter which is the "opposite" of matter per say.

Before we go into antimatter, lets look into what matter is made of. Matter is made of 'atoms and molecules' which contain protons, neutrons and electrons. These are made up of different kind of quarks such as up quark, down quark and strange quark to name a few. So technically, we can say that matter is made of particles such as quarks.

Anti-particles are basically particles which have the same magnitude for their properties but have the opposite sign for the specific elementary particle. For example, a positron has a charge of +1e with the same mass of an electron and is therefore considered as the antiparticle of the electron.

Matter and antimatter are said to annihilate (completely) into energy if they come in contact. For example, let's say a mass of 10kg antimatter is coming towards earth. When the antimatter comes in contact with earth(made of matter) 10kg of earth will be destroyed along with 10kg of antimatter and energy will be generated. This energy can be calculated by the formula e = mc^2. Of course this implies that in this scenario, 9 * 10^17J of energy (which is a very huge amount) will be produced along with the annihilation of both the matter and the antimatter. Radioactive rays are also released but that is a topic for another day.

Currently many scientists are trying to find a way to store matter however it cannot be stored in a container as the result would be annihilation. Therefore, some scientists are trying to use magnetic and electric fields as the antimatter containers instead however success is limited.

Thanks guys and more will be coming soon on a variety of astronomy topics.

The Hand of God?

Don't you think that this amazing nebula looks like the hand of God? Some people say it is a coincidence. Is it or not is your own choice but you have to admit if it is a coincidence then it is an amazing one as it looks like god is pushing his blue hand into a pit of fire.

This nebula was formed by a cloud of gas that surrounded a neutron star called PSR B1509-58, or B1509 for short. Neutron stars will be explained in the video below, but in short it is a star that is burning out and collapsing into itself.

The photos have caused several religious debates, and at the end you have to wonder this is proof that God exists or not.

The Jade Rabbit

China will launch its first ever moon rover mission on Monday.A rocket carrying the spaceship named "Jade Rabbit" will blast off at 1:30 P.M. If successful, the launch will be an amazing help to China's space exploration programme, which aims to create a space station by 2020 and eventually send someone to the moon.

It will make China only the third nation to soft-land a spacecraft on the moon. Beijing sees its military-run space programme as a great thing to prove that China is amazing in technological research and to promote themselves. China has previously sent two probes to orbit the moon early in November, Beijing offered a look into its secretive space programme when it put a model of its moon rover on public display.

The rover was later named "Yutu", or jade rabbit, following an online poll in which more than three million people voted.The name comes from an ancient Chinese myth about a white rabbit that lives on the moon as the pet of Chang'e, a lunar goddess who swallowed an immortality pill.

Doomed European Satellite

The recent news is that a doomed European satellite is about to hit earth very soon.  The European Space Agency says that one of its research satellites that ran out of fuel will most likely crash to Earth into the ocean.

The agency said Sunday the crash is expected to occur between 6:30 at Sunday or 12:30 on Monday."with a very high probability, a re-entry over Europe can be excluded

."Spokeswoman Jocelyn Landeau said the satellite, GOCE, will mostly disintegrate as it comes down and "we will have only a few pieces which could be 90 kilograms at the most."

NASA is telling everyone to not worry because it is more likely to win the lottery 250,000 times in a row than get hit by any part of the satellite debris. This satellite had survived for triple of the time expected for it to survive

Quantum Teleportation

Going slightly of topic, I have to say that the new method of transportation called Quantum Teleportation is absolutely amazing. This was first attempted in 1997 but did not work at that time. It gives a person the ability to teleport itself or anything else. It is truly an amazing thing. Now I will let a video tell you the rest about Quantum Teleportation in detail.

The Russia Meteor Incident

The recent news is that on Friday morning (Feb.15), the Chelyabinsk region of Russia was shocked by a giant fireball shooting across the sky. 

The explosion, caused by a small meteoroid entering the atmosphere, injured hundreds as it destroyed the windows which sent glass flying all over.

In a way the videos of the glass and fireball gave the scientists the exact location and size and shape of the meteorite and it also gave the scientists help to figure out what happened

Diamonds on Other Planets

Researchers have now found out that the atmosphere of the planets Saturn, Neptune, Jupiter, and Uranus have perfect atmosphere, temperature, and pressure to have carbon in the form of an diamond.

The proof was presented three days ago at the American Astronomical Society Division for Planetary Sources conference in Denver. It has been found that Neptune and Uranus have more gems than Jupiter and Saturn.

These diamonds have been found to be a little more dense than the earth diamonds. It has been found out that one of the reasons by which diamonds were created is the lightning in the planets containing diamonds.

Johannes Kepler

Today I am going to write about the astronomer Johannes Kepler's history, and in my next three blog posts, I shall share information about his three laws.

Kepler was born on December 27th, 1571, in Weil der Stadt in Swabia. His grandfather, Sebald Kepler, was a  craftsman who served as mayor of the city. His other grandfather Melchior Guldenmann, ran an inn and was mayor of the nearby village of Eltingen.

His father, Heinrich Kepler, was a soldier who he did not like, and he also did not like his mother. Throughout his whole life Kepler had many illnesses.

Kepler lived with his grandparents until his parents shifted. Then he started studying in a Latin school and turned out to be a great mathematician. After that he followed astronomy and found his love for it. He also worked in the areas of astrology and optics.

NASA is Trying to Capture an Asteroid

NASA has always wanted to catch an asteroid but thought it was too expensive and therefore never tried. But now they found out that capturing an asteroid may not be as difficult or expensive as NASA had thought.

They are currently planning out a bold mission to snatch an asteroid and drag it to a stable orbit near Earth, where it could be visited repeatedly by astronauts for scientific purposes. 

The best way they think to do this is to chase down one of the "mini-moons" that go around our planet temporarily before going back off into deep space.

New Alien Planet

A nearby alien planet six times the size of the Earth is covered with a water-filled atmosphere that includes a strange plasma form of water. Astronomers have determined that the atmosphere of super-Earth Gliese 1214 b (which is the planet's name) is likely water-filled. 

However, this new planet is not like Earth meaning it can't allow human conditions. The high temperature and density of this planet gives it an atmosphere that is a lot different than Earth, so therefore no one can live there.

Although it is still a great discovery because it proves that water does exist outside our planet, it also proves that there may be aliens.

Ten New Black Holes

The recent news is that ten extremely large black holes have been found with the help of a super telescope. The super telescope is a black hole hunting telescope called NuSTAR (Nuclear Spectroscopic Telescope Array). Although they discovered the black holes by accident, it is still a great discovery. The observatory is called the x-ray space observatory. It is an achievement because this discovery shows that there is so much of the galaxy that we do not know about.

Before the discovery there used to be mysterious sources of light which have now been identified as the light from one of the black holes. NASA uses a cosmic x-ray background so they can identify which thing is what in space. For example, a black hole's color in the cosmic x-ray background is purple. This discovery also proves that the bigger the galaxy, the more black holes.

This proves, as I said, that there are many other black holes and galaxies. It also proves that the universe is infinite, and it is continuously growing.