Hypothesis  

Since matter and antimatter are supposed to be polar opposites then the same equations that apply to matter should apply to antimatter, however using the basic energy equations it does not seem possible to have negative energy: My question is why?

 

My hypothesis is either that matter and antimatter are not truly polar opposites and that physicists have already developed equations for antimatter that I am unaware of,or that the mass for antimatter must be negative. I am thinking this because many energy based equations have a lot to do with mass or momentum, momentum being speed times mass.

I will go into more detail about this later on in the project, but essentially if the mass in an equation for energy is negative, it leads to the possibility of a negative answer, since most energy equations are primarily based on multiplication or division. I am going to explain more about my question and hypothesis later in this project, but I am going to discuss my method right now. 

Project Method

 

In order to answer my question I am going to:

 

1. First, do a surface level Google source and check reputable sources to see if there is a simple answer to my question. An example of a reliable source I used is the CERN website.

 

2. Second, I will also read a particle physics textbook¹ to help better understand my question. This textbook gives me a better understanding of subatomic particles, the standard model of matter and particle accelerators, to list a few.

 

3. In parallel with the particle physics textbook review, I will be learning more about the foundations of relativity, in order to better understand the origins and answers to my hypothesis.

 

4. After a significant amount of time with the textbook, I will begin looking at case studies, such as experiments, papers and other sources that discuss the topic of the mass and symmetry of antimatter. 

 

5. Based on the case studies, I will develop a conclusion as it relates to my hypothesis.

 Sources used (3) (19)

Examining case studies  [Sources used (4)] *it is recommended to read the data section before this one

In this section of the project I will be explaining how I will be examining case studies, as well as the list of case studies I will be looking at. The case studies will mostly be experiments on antimatter, as well as some theoretical work, and maybe other sources. I will be looking at sources that discuss the mass of antimatter, and how it relates to symmetry. 

 

However, there may be some sources I look at that will focus entirely on symmetry towards the end of the list. I will be looking at the case studies in an attempt to relate them to my hypothesis. Specifically, if the case studies conclude that matter and antimatter are not polar opposites, then it may turn out that antimatter would have different equations to calculate its energy, but if it suggest that matter and antimatter are truly polar opposites, then it would suggest that mass for antimatter may be negative. 

 

Once I finish examining the case studies I will take further steps to arrive at a true conclusion. The interviews I do are completely separate from the case studies as they are more directly related to arriving at my conclusion rather than just doing the research. I will be looking at seven case studies. They are (in no particular order): 1) ATRAP on the magnetic moment of antimatter 2) LHCb experiments that observes a new different between matter and antimatter 3) ALPHA that studies charge of antihydrogen 4) Cronin and Finch’s discovery of a difference between matter and antimatter 5) ASACUSA study that weighs antimatter to one part in a billion 6)  ALPHA’s laser spectroscopy of antihydrogen 7) and ALPHA-G studies on antimatter and gravity.

 

ATRAP magnetic moment  [Sources used (7)(8)]

 

On March 25, 2013 in Geneva, Switzerland,  the ATRAP (Antihydrogen TRAP) experiment, which was conducted at CERN, attempted to make the most precise measurement of the magnetic moment of antimatter and they succeeded. Essentially the magnetic moment is how likely an object is to align directly with a magnetic field: the higher the magnetic moment, the more the object is affected by the magnetic field and vice versa.

 

ATRAP often focuses on trapping and measuring antihydrogen which is an entire antiatom, but for the magnetic moment experiment they just used antiprotons, or just an antiparticle. The main purpose of conducting this experiment was to better understand how antimatter works, however the results of this experiment may have challenged CPT symmetry and the standard model of matter if they got a result they did not expect. This is because, hypothetically, matter and antimatter should have the same magnetic moment just reversed

 

The physicists conducted this experiment by trapping an antiproton between many electrodes; the particle found itself sandwiched between two copper electrodes and suspended between 2 iron electrodes. The results of this experiment concluded that matter and antimatter have the exact opposite magnetic moment, at least as far as they can tell. This means that the experiment did not dispute CTP symmetry or the standard model of matter and it also means that the standard physics equation should apply to antimatter since this experiment suggests that matter and antimatter are polar opposites. 

 

LCHb observes a new matter-antimatter difference 

[Sources used (9)(10)(11)]

 

In Geneva on April 24, 2013, the LHCb collaboration working at CERN  submitted a paper on the decays of a particle knows and B0 or the B-meson and also D-mesons, which are very similar to B-mesons. The difference they measured had only been measured in 4 other particles and it was concluded that the difference did violate fundamental CPT symmetry, speci- fically the CP part. The D-meson and the B-meson are made of different quarks; the D-meson is made of one charm and one top and the B-meson is made of one strange and one bottom. 

 

The really interesting part of this experiment is the D-meson because for the last 40 years, the B-meson was the only detected meson to show these particular CPT violations; this was assumed to be because of its quark makeup, but the recent D-meson discovery has challenged all of that. One thing to note is that initially both the B and D meson will initially decay into a Kaon and a pion, often represented by K and π. 

 

The difference that was detected is that when the B mesons decay, they become a negative Kaon and a positive Pion, but CPT symmetry says that if you reverse the charges in the decay, the symmetry should hold up, however when, if measured, charges where reversed, which showed there was an error of 0.27 or a whole 27%. This is a rather large difference and a big problem in regards to CPT symmetry, specifically the CP part. This experiment is related to antimatter because when you reverse the charge of the decay, even just mathematically, you are predicting the antimatter version of the decay, thus this experiment also suggests that classical physics formulas may not apply to antimatter.

 

 

 

ALPHA studies the charge of antihydrogen 

[Sources used (12)]

 

When physicists examine antihydrogen, CPT symmetry states that all of anti hydrogen’s properties must be opposites or reversed. When we look at neutral atoms made up of matter, we can determine that their charge is neutral to 21 digits, and now ALPHA is measuring the same for neutral antiatoms. 

 

The first experiment ALPHA did was able to state that antiatoms, specifically antihydrogen, was neutral to 8 digits, however, their most recent experiment states that to 10 digits, which may not seem like a large difference, but it is a huge advancement in the certainty of the measurements. 

 

When the measurements were done by ALPHA, they were able to conclude that an antiatom, that should be neutral, based on the principle of CPT symmetry, was indeed neutral. The results of the experiment suggest that matter and antimatter do follow the basic laws of CPT symmetry. This suggests that basic formulas for matter should also apply to antimatter. 

 

The results of the experiment were found by applying a magnetic field to antihydrogen escaping a trap. By applying the magnetic field, they could force charged atoms to move to the left or to the right. Physicists were then able to determine the change of the atom with high precision  by measuring where the antihydrogen atom contacted the apparatus when under different magnetic fields. Charge is a very important part of CPT symmetry, especially as it is the first word in the acronym and understanding its charge is an important factor when considering antimatter matter symmetry. As far as we know, or can measure, antimatter, at the atomic level, does follow the laws of CPT symmetry.

 

Cronin and Finch discover a new matter- antimatter difference   [Sources used (13)(14)]

 

This is one of the earliest case studies, I will be looking at a case study done by James Cronin and Val Finch done in 1964. This study showed evidence of one of the earliest matter and antimatter differences ever detected. The experiment they did involved neutral K-mesons or Kaons. Kaons are special mesons that consist of one half matter and one half antimatter. They started by having two different types of kaons. The first is long lived kaons; these often live for 5.2 x 10 to the power of -8 seconds and they decay into three pions. The second type are short lived kaons and they live for 0.89 x 10 to the power of -10 seconds and decay into two pions. 

 

Cronin and Finch conducted their experiment by shooting kaons down a shaft and the lifetime of the kaon would determine the wavelength of the beam. When they did their experiment they shot beams of kaons down a shaft; based on previous assumption, they thought the short lived kaons would decay before they reached the detectors so they would only detect long lived kaons.  However they did detect short lived kaon decays. This meant that there was a difference in matter and antimatter. 

 

It turned out that the ratio of short lived kaons to long lived ones was 1 to 500. This was the first ever difference between matter and antimatter that was detected since the discovery of antimatter. Cronin and Finch won the Nobel prize for the violation of CPT symmetry in regards to neutral Kaons in 1980. Their research suggests that maybe matter and antimatter are not polar opposites, so maybe classical physics equations do not apply to antimatter.

 

ASACUSA and antimatter weight 

[Sources used (15)]

 

Before I discuss the ASACUSA experiment it is important to know that ASACUSA was experimenting with antiprotonic helium which is essentially one electron and one antiproton orbiting a nucleus of two protons and one or two neutrons. This experiment was conducted on November 3, 2016. Scientists measured around two billion atoms of antiprotonic helium when the atoms were cooled to 1.5-1.7 degrees above absolute zero. The measurements that were made were measured to compare the regular proton counter parts to the measured antiprotons. Going into the experiments, it was important to note that based on CPT symmetry, the particles should have the same weight. 

 

The measurements were done by using spectroscopy, which then shines a laser into the atom and by turning the laser to the right, scientists caused the antiproton to make a quantum jump within the atom. From the frequency of the jump they were able to calculate the mass of the antiproton relative to the electron. The results of this experiment showed a similar conclusion to other studies done and suggested that matter and antimatter do follow CPT symmetry due to the mass of the particles being the exact same as the mass of the antiparticle, at least as far as we know. The fact that the mass of the anti particle and particle are exactly the same suggests that we should be able to use classical physics equations to determine the mass of antimatter.

 

ALPHA-G antimatter and gravity 

[Sources used (16)]

 

Last year, September 2023,  ALPHA-G was the first experiment to measure the effect of gravity on antimatter, specifically antihydrogen. Unlike the other case studies, this experiment is questioning the Einstein equivalence principle. CPT symmetry states that an atom falling on earth would react in the same way as an anti apple on an anti Earth. The equivalence principle that is being discussed here states that antimatter and on Earth should react the same and matter on Earth. The one problem here is that if the gravity on Earth pushes antimatter away from the Earth, then it would mean that gravity pushes antimatter away and that would explain where all the antimatter has gone. 

 

After all of the tests were done it stated that antimatter does fall down when experiencing earth's gravity. While this may not relate to CPT symmetry directly, it does disprove the idea that antimatter is not visible in our universe due to being pushed away by antimatter, thus adding to the problem with CPT symmetry with regards to antimatter. This was conducted similarly to ATRAP where physicists released the anti hydrogen from the trap, but instead of using magnetic fields to measure charge, they just measured how the antiatoms reacted to gravity. They did use a magnetic field, but that was to quantify the gravitational force acting on the anti atom. Since it was concluded that antimatter reacts with gravity the same way matter does, we are still left with the question of why there is no antimatter in our universe.

 

 

ALPHA laser spectroscopy of antihydrogen 

[Sources used (17)]

 

While the title may sound long and complicated, the measurements that this experiment  recorded are very simple: the color of antimatter. This experiment was completed on December 19, 2016 in Geneva, Switzerland 

 

When electrons orbit the nucleus of an atom, they will move from one orbit to another and emit light as a specific wavelength, which can be interpreted as color. Due to this, spectroscopy can be used in many ways in science, specifically in Physics and Chemistry. Spectroscopy can help us understand the internal actions of the electrons within the energy level of atoms, and even antiatoms. 

 

One last important fact to note is that every element releases a different wavelength when its electrons are “excited” in this way. Due to hydrogen being the most abundant element in the entire universe, we have a very good understanding of the light spectrum it releases, which is why antihydrogen was the first antiatom to be measured. 

 

The point of the experiment was to determine the color of the wavelength of the light emitted by antihydrogen. The experiment ended up concluding that the light emitted by antihydrogen is the same, at least in terms of color, when compared to the light emitted by hydrogen. This is another example of an experiment that produced a result that agrees with CPT symmetry. Due to the results of this experiment it would remain a reasonable assumption that classical physics equations would apply to, at least, antihydrogen.

 

 

Summary 

 

This project has gone places I never expected. As it turns out antimatter has its root all throughout particle physics and is essential to our understanding of many aspects of our world. To summarize, all of our knowledge of antimatter does not come from the natural universe, but it comes from highly advanced labs and particle accelerators, which run based on the principles of magnetism and relativistic speeds. 

 

Antiparticles are not just anomalies anymore; they have been included in many interpretations of the standard model of matter. Much of matter and antimatter follow the laws of CPT symmetry, specifically mass magnetic moment color and charge are all the same, however, when it gets down to particle decay, things start to get more complicated.

 

A couple interesting things to note before I move on are the fact that matter and antimatter have many hypothetical differences that cannot be detected, but can be explained, like the negative energy is not measured but it was how antimatter was discovered. Also many antimatter particle decays, like seen with the b-meson, and this may yield strange results that must be explored. 

 

Another important detail to note is that matter and antimatter react the same way to gravity, meaning one of the biggest problems with CPT symmetry is where all the antimatter went. If there was a large enough patch of antimatter in our universe, we would constantly see the annihilations of matter and antimatter, but we do not. It is also important to note that the mass of antimatter has been assumed to be positive by many of the scientists that conducted the experiments from the case studies. There are two other important things I need to talk about before I get to the conclusion, which are the important quantum concepts and a little bit more about CPT symmetry.

 

Interview with Pooja Woosaree and Tim Friesen, March 11, 2024.

Dr Tim Friesen (TF)

Tim Friesen has been studying antimatter and antihydrogen for more than 10 years, starting as a PhD student at the University of Calgary (completed 2014). Following his PhD, he moved to Geneva, Switzerland to work full-time on the ALPHA experiment at CERN on the border of France and Switzerland. In 2018, Tim rejoined the University of Calgary as an Assistant Professor in the Department of Physics and Astronomy and continues his work with ALPHA with a focus on antimatter traps, microwave experiments with antihydrogen, and gravitational free-fall measurements.

Pooja Woosaree (PW)

Pooja Woosaree is a fifth year PhD Candidate with Dr Timothy Friesen’s group. She received a Bachelor of Science with Specialization in physics degree from the University of Alberta in 2014, and completed a Master of Science in physics degree from Laurentian University in 2019.

Upon finishing her BSc, Pooja went into industry. She worked as a laboratory technician for two years before being encouraged to pursue a graduate degree. This was the beginning of many travels to various physics laboratories around the world which include TRIUMF, SNOLAB, and CERN. Pooja's latest project involving antimatter research, alongside an international collaboration at CERN, has proven the free fall direction of antimatter. This result is a great contribution towards fundamental physics research, and another step towards a better understanding of our Universe.

 

Interview Questions

 

1. What is the most important thing to understand about CPT symmetry? 

    PW: It's a fundamental symmetry of nature, Understanding Charge Parity Time. 

    TF: As far as we know, it’s the fundamental symmetry between matter and antimatter; if you take a CPT transformation you should get the antimatter version and it should act the same. 

 

2. How does antimatter relate to classical physics formulas?

    PW: I think that is an interesting question. It's a matter of studying the problem is the best way to solve it. What experiment can you devise to test this? The math may not be the ending. 

TF: The interesting thing about what we do, [is] we trap antihydrogen matter. When we try to model the behavior of the antimatter, we use the classic equations of physics, and it works very well to describe the antimatter. 

 

3. What is the best way to think of matter antimatter collisions?

    PW: Two different colored balls that come together; they do explode, not just energy, other particles form. I guess the best way to think about this, [is] when two ducks explode, it's not just a burst of energy, I can produce other smaller ball or ducks 

 

4. What is one of the most common misconceptions about antimatter? 

TF: One of the most common misconceptions is that antimatter and dark matter are the same thing; we may have anti dark matter, but it is not the same thing as antimatter. 

 

5. Where do you think all of the antimatter is in our universe?

PW: When we look at this problem we are under the assumption that all the antimatter is gone, it all annihilates, and all that's left with is matter. There is a theory it is in a pocket of our universe which is a possibility; I personally don't know where it all is 

 

6. What do you think the most important milestone in antimatter research was?

    TF: The formulation of the Dirac equation, combining special relativity and quantum to make antimatter.

    PW: I think Tim’s answer is great; I think it is the discovery of the first antiparticle. t really solidified the search for antimatter  

 

7. What do you think would be the biggest discovery to make in antimatter

    PW: The ultimate thing we could discover is why we have more matter than antimatter; it could explain why we are here

    TF: Exactly the same, who knows what comes after that? 

 

8. What do you think of the Dirac equation, do you think it predicted antimatter directly?

    TF: that's a hard question; It's a hard problem. I think the idea of negative energy of antimatter, I think it's the initial answer to the result. we don't need to think of energy as negative with antiparticles. I would say they had a negative energy in the typical sense. 

    PW Could the Dirac equation predict neutrinos, which have no charge? 

 

9. Do you think antimatter mass can be negative, why or why not? 

    PW: I am actually not sure how to answer, no. 

    TF: The negative answer was a particle was a reverse spin and direction, that then got a negative answer; the mass from force and gravity mass are the same. 

 

10.  What do you think of my conclusion, that antimatter could experience negative time? Is it possible or not? Why or why not? 

    PW: Exactly how I think of it; I think it's true 

    TF: I think antimatter goes forward in time like everything else, saying you flip chart, no big deal, flipping positions, no big deal, flipping time, well that's a problem; mathematically it's just putting a negative in front of a number. It is like antimatter does what matter does but backwards. 

 

11. Why did you join the ALPHA project? 

    PW: I met Tim at a conference; he talked about ALPHA and I applied to UofC and I ended up working at ALPHA as well 

    TF: I met Rob [Dr. Robert I. Thompson, U of C]and I got a chance to work on antimatter and I got excited and I agreed. 

 

Most important point

Tim and Pooja made the point that antimatter does probably experience time negatively, but I have taken that a step further in the final conclusion, just based on the research I did. 

 

 

 

What is Antimatter?  

 

The simplest way to describe antimatter is that it is the polar opposite of matter. Most antiparticles and antiquarks have the opposite charge and spin compared to matter and all of the properties should have the same magnitude; for example the antiproton is a negative charge of -e and the anti electron, or positron, has a positive charge of +e. This principle also applies to quarks which I will get back to later. here is one key problem with antimatter and it has to do with CPT symmetry, or Charge Parity and Time Reversal symmetry. CPT symmetry is essentially saying that when you reverse charge parity and time the physics would not change; this is what tells us that all other characteristics of antimatter and matter are the same except for charge and parity, often represented by spin, also but could be other things. 

 

CPT symmetry is also why every time we create a matter particle, we also create an antimatter particle; by create, I mean transforming energy into mass, which can be done here on Earth by using a particle accelerator, but more on that later. However when we convert energy into a particle in an accelerator, we always also create an antiparticle. This follows CPT, but CPT symmetry also states that when the universe was “created” there would have been an equal amount of matter to antimatter, but this obviously is not the case. If it were the case, then there would constantly be collisions between matter and antimatter across the observable universe which would be easy to detect. This is because when matter and antimatter come into contact, they annihilate each other and convert all of their mass into energy. These explosions are easy to detect because they release more energy like that of a nuclear explosion. This is because nuclear explosions happen because of the splitting or fusing of nuclei converting a fraction of the mass of the nucleus into energy; when this is done with a heavy element, it can release large amounts of energy. When antimatter and matter particles annihilate they convert all of the mass of the nucleus into energy, meaning they release exponentially more energy when compared to a nuclear explosion.  The reason for this is because all of these properties are opposite so they cancel out causing the annihilation. 

 

Sources used (19)

 

 

How Did We Discover Antimatter?

 

Antimatter was discovered after Einstein came up with relativity and Erwin Schrodinger and Werner Heisenberg came up with quantum physics equations. Einstein's relativity equations describe an object moving at very high speeds and the quantum equations describe an object that is very cold and very small. I will explain more about both states as later in the project. 

 

For a while these two states, being relativistic and quantum, were thought to be mutually exclusive, but then someone realized you could have a small cold object going at a relativistic speed. This meant you could combine the equation for relativity and quantum. This was done by a British physicist named Paul Dirac in 1928. He combined the two equations and the result was surprising. Einstein's equation for relativity was E=mc2 and p=mv as well as many concepts from relativity which are brought again in this project when I talk about relativity, and the quantum equations were E=hv, E=pc and p=hvc. All of the equations and a little bit of advanced math allowed for the equation E2=p2c2+E2 and after a little bit more math involving relativity we got E=mc2 which gives us the equation E2=p2c2+m2c4. When solving for E you get the equation E= (square root) p2c2+m 2c4 This equation has both a negative and a positive solution. For a long time physicists only considered the positive solution for energy and considered the negative solution to be a mathematical anomaly. But then someone suggested that the negative value may be something. Thus the idea for antimatter was born. 

 

It took another 4 years for antimatter to be proven by a physicist named Carl Anderson officially discovering the positron. The Dirac equation states that antimatter must have negative energy, but our tool we use to measure antimatter states the value as positive, but that is merely a technical limitation and not an indication of dirac being incorrect. It would be impractical to develop new technology to give the negative value if we can just add the negative ourselves. 

 

 

 

Logical Problems with Antimatter

I have brought this up already, but antimatter and matter are supposed to be polar opposites. All particles and their antiparticle opposites have the opposite spin and charge to each other.

If we only look at the charge of a particle, a good way to conceptualize would be thinking of electrons and protons. A better example would be quark pairs, like up and down and top and bottom,

but I will explain those in more detail later. One of the statements I suggested in my hypothesis was that the mass for antimatter may be negative;

this is because since the reason matter and antimatter annihilate is that all of their attributes cancel out, why do their masses not cancel out? 

 

This is a logical problem with my current understanding of antimatter and there are multiple ways it could be solved. I will be looking for a solution to this going forward in my research.

One of the main ways I can think to answer my question would be through analysing case studies. More specifically,

if most case studies point to matter and antimatter not actually being polar opposites, then it would be reasonable to say that they would require their own equation to calculate energy,

which was another point I made in my hypothesis. However if most case studies conclude that matter and antimatter being exact polar opposites,

then it may be then there is some attribute about antimatter that I have interpreted wrong, such as mass.

There may also be another solution I could come up with after more research is done towards the end of the project, but that is a topic for later in the project.

 

Mathematical “Problems”

 

Since matter and antimatter are polar opposites, the same equations used to calculate properties of matter and antimatter are the same, just yielding different results.

We know that the Dirac equation gives antimatter a negative energy value, so for now, I will be looking at energy examples. Let's take a basic (non-relativistic) energy equation 

 

Ek=1/2mv2 

 

This first equation is for kinetic energy of an object being E_k and m is object mass with v being its velocity.

Now an object made of antimatter should produce a negative answer for energy as shown by the Dirac equation. Now let's try to get a negative Energy 

 

Ek=1/2mv2 Ek= 1/2 (3) (4)2 Ek = 24

 

In this equation, we assume a positive mass and a positive velocity, meaning the object was moving forward. This equation could not give us a negative result for energy. 

 

Ek= 1/2 (3) (-4)2 Ek= 24

 

In this equation mass stays the same, but we say that the velocity of the object is negative, meaning it is traveling backwards.

However due to the squaring of v the negative goes away and we are left with the same answer. 

 

Ek=1/2 (-3) (4)2 Ek = -24

 

It appears that the only way to get a negative energy using this equation is if the mass of antimatter is a negative value, but physics says that is not the case.

This same logic holds up for many other equations, however they all act similarly to the one I showed here so I won't go into too much detail about them right now.

 

Essential knowledge of particle physics

 

The most important piece of knowledge in regards to particle physics for this project is the standard model of matter.

The standard model of matter classifies anything that is smaller than an atom. In the standard model, there are essentially 4 categories that something can fall into: 

bosons, fermions, leptons and hadrons. Something cannot be a fermion and a boson and something cannot be a lepton and a hardon.

A boson is something with an integer spin or a spin of a whole number. A fermion is something that has a fraction spin, which is why a particle can be both a boson and a fermion. A hadron is anything made of quarks and we do not actually know what leptons are made of. 

 

Quarks are the smallest currently known building block of life and there are six types of them: up, down, strange, charm, top and bottom.

Up and Down are the lightest of the six and up is positive and down is negative. Top and Bottom are the heaviest and top is positive and down is negative.

Strange and Charm are in the middle, but they are the most interesting: strange is negative and charm is positive. There can be antiquarks as well. 

 

There are also only six known leptons: electrons, tauons, muons, electron neutrinos, tau neutrinos and muon neutrinos. All leptons have an antimatter variant.

There are other particles that fit into this model including gluons, which are responsible for the strong force, gravitons which are responsible for gravity, photons, which are light and many other bosons responsible for  weak interaction and cosmic radiation. 

 

  

 

What you need to know about relativity 

 

One of Albert Einstein's biggest contributions to science was the idea of relativity. Relativity governs objects moving at very fast speeds, approaching the speed of light.

Essentially Einstein's theory of relativity allows for time dilation, which means that if you were in a spaceship and were approaching the speed of light, then time would move faster for you. 

 

Another important detail of relativity is that physics is the same in every frame of reference, which essentially means that no matter what point of view you observe the universe,

the laws of physics must be the same. The most important part of this detail is that the speed of light is the same in every frame of reference.

The formula that gives us the details of time dilation in relation to speed approaching the speed is complicated, but it can be simplified using linear systems and some basic physics concepts,

like the fact that the speed of light is the same in every frame of reference. 

 

I did briefly talk about this equation early when I was talking about the Dirac equation, however, I did spend a bit more time on the quantum equations there. The exact equations of relativistic speeds are not so relevant to the project; it is just important to understand two things. First, time passes faster the closer your speed gets to the speed of light, often noted as c. Second,

there is another important equation which is 

 

E=m(knot)/ (square root of) 1 - (v/c)(to the power of)2

 

This formula essentially states that as the speed of an object approaches the speed of light, or c, the more energy it loses as mass. As seen here 

 

E=m(knot)/(square root of) 1 - (10/30)(to the power of)2   E=m/0.9    <   E=m (knot) / (square root of) 1-(1?/0) (to the power of) 2  E=m0.999

 

Where c = 30 Mdam(mega decameters)/s

 

How do we learn about antimatter? 

 

I said that one of the fundamental problems with antimatter is that we have not found much of it in nature. Some natural decays allow for positrons to form, however,

they annihilate very quickly.

The reason that antiprotons do not appear naturally is that they are so heavy and require so much energy to form. This leads to one big question: how do we study antimatter? 

 

Since it is very hard to find antimatter we have to find alternative methods of studying it.

The answer to this question is particle accelerators with the primary candidate being the many colliders found in CERN, in Geneva, Switzerland. 

 

I am going to be studying case studies later in the project and I am going to briefly explain how particle accelerators work so we can all have a better understanding of the experiments.

Firstly, particle accelerators work by accelerating particles to relativistic speed levels. This is done by using RF cavities. Particles are accelerated by using oscillating electric fields.

This is achieved by having two segments in the cavities that have opposite electric charges and they oscillate back and forth between the positive and negative charges.

This causes the particle to be pulled in due to one charge in the front and then pushed out by another charge in the back and the oscillations make sure this process is smooth.

One RF cavity is not enough to get to relativistic speeds and this means we either linearly line up cavities, or make an oval and use the same cavity multiple times.

The particles are moved in a circle using a magnetic field. Once the particles are accelerated to relativistic speed, which I will explain below,, they can collide with either a fixed target,

like a wall, or with another beam. Once they collide they have so much kinetic energy that escapes the particle that it has to go somewhere.

Hopefully there is enough energy there that will convert into mass or a physics particle, more specifically a particle antiparticle pair, meaning CPT symmetry withstands. 

 

We don't have a supply of antimatter because some antiparticles are unstable and will often decay first into other mesons, and then eventually into quarks and/or photons;

decaying into free quarks is a purely theoretical idea and has not been observed yet. Any form of matter that is stable also has its antimatter counterpart that is also stable; however,

even stable antimatter does not last long on earth because it would inevitably collide with matter and annihilate. Photons also do not have an antimatter counterpart as far as we know.

We have many different methods of measuring attributes of the products of particle collisions, but these vary greatly depending on the experiment. Some methods include bubble, gas,

cloud, and spark chambers and even Cherenkov detectors. 

 

Sources used (19)

 

What does it mean to violate CP symmetry 

[Sources used (18)(19)]

 

CP symmetry only refers to charge and parity; the reversing of charge is often referred to as creating antimatter. It is important to note that it does not create antimatter; it just refers to the properties of the antimatter equivalent of an object. Also parity symmetry is mostly in regards to location. 

 

If you violate CPT symmetry, it can cause a lot of problems and this can relate to the relativistic speeds. One assumption that was made during the relativistic speed section was that all frames of reference follow the same laws of physics; if CPT symmetry is wrong, then based on your frame of reference, physics could be different. For example if I am on a bus and you are on a sidewalk, we are both sucked to Earth by gravity, but if CPT symmetry was false, we could both interact with gravity in many different ways. That is a very simple example, but if CPT symmetry was false, every physics principle would need to be tested from every single frame of reference and that would be impossible. This is why CPT symmetry is so important. 

 

One thing I need to establish is that CPT symmetry cannot be disproven; we have already given proof it is real. The only thing that could change it is we realized it is incomplete. However, we have already based so many calculations of this symmetry that it could still cause many problems throughout all of physics if something major about CPT symmetry is incorrect. In conclusion it is highly likely that most of the classical physics equation should apply to antimatter with very little to no differences.

 

What do you need to know about quantum? 

 

Before I get to the conclusion, there are a couple quantum concepts I must explain. 

 

Firstly, the quantum concept of wave particle duality, which essentially means that anything that is thought to be a particle, like a proton, can act like a wave, like a photon, and vice versa. This has already been seen at the beginning of this project when we derived the Dirac equation and we used a few quantum wave equations; specifically we assumed that photons have mass like a particle even though you have to be a massless wave to travel the speed of light. More specifically, when a photon is a particle, its energy is given by Planck's constant times the frequency of the light: the more blue the light, the more energy the photons have. 

 

Secondly, In general quantum, any measurement can only have specific results for a measurement, determined by the system. All electrons are in quantum states and if we feed them a photon of a very specific energy, we can force the electrons to change state within the energy level. If CPT symmetry holds then the same energy given to an atom and an antiatom pair, then the same change should be seen in both atoms, if not it becomes a CPT violation. Each atom needs a specific energy amount for its electrons to change state. By measuring how much energy was required to convert the states of the electrons in a specific atom, scientists are able to classify the atom AND would hypothetically be able to classify the anti atom, as long as CPT symmetry holds. Now we are ready for the conclusion.

 

 

How I got to my conclusion 

 

In this document, I am going to talk about how I got to my conclusion. I was thinking about my original hypothesis and I realized the one place my mass idea was wrong: gravity. You see, essentially gravity is the mass of the object being affected by gravity, times the mass of the effecting object, times the acceleration due to gravity, which essentially means that if you have antimatter on Earth, it should fall up, but we know it does not. 

 

Then I started thinking about the CP symmetry, and more importantly, about the T I left out. What if antimatter goes backwards through time? In my actual conclusion I will go into more of the evidence I thought up but, for now, I am just going to explain the gravity. If the acceleration due to gravity on Earth for matter is determined by a=v_f-vi/tf-ti where vf is more negative then vi leading us to a negative overall velocity divided by time, gives up a negative acceleration due to gravity, times the two positive masses of Earth and the objects get us a negative force of gravity which lead to objects falling down. 

 

However, if antimatter experienced negative time, then it would be a negative velocity divided by negative time, but it would be multiplied by a positive mass of earth and a negative mass for antimatter which would still get us a negative force. This conclusion is more of a better hypothesis based on the data I have learned about rather than just an idea I had before my projects. In the conclusion section, I am going to talk about how my theory would affect many things, such as the big bang, why we can observe antimatter, and antimatter annihilation. 

 

However, I am also going to need to establish the one thing that needs to be researched for my theory to be true, which I will get to in the next section. One more thing before I get to my conclusion is that in the interview I was told something interesting about antimatter and time which I will address in the conclusion.

 

Conclusion 

 

Before I proceed I am going to say that I have no credentials to state that based on my conclusion, anyone in the scientific community is wrong. My research was done with the resources that are available to a high school student and the people I interviewed said I asked questions that are asked to PHd candidates. 

 

This is the conclusion I got to what I am going to phrase as a hypothesis for an impossible-to-do-experiment. My conclusion states that antimatter experiences time in the negative direction. I am going to provide some evidence that states it is not brought up during the interview. 

 

Firstly, in the interview with Dr Tim Friesen, he said that it helps our understanding of antimatter to give it a negative time value, but when it comes to gravity, it does not help without a negative mass; this is the main reason I am not changing my conclusion at this moment. 

 

The first way that I can support my conclusion is that antimatter annihilates by its properties canceling; as Dr. Tim Friesen said, the negative energy is hypothetical, but if mass was positive. the masses of the particles would be left, which we know is not the case. The second way I can support my conclusion, is that Secondly, if we think about my conclusion, it could say that the reason antimatter is not in our universe is because at the time of the big bang antimatter took up the negative time and matter took up the positive time. The one way I can explain tims point of antimatter experiencing positive time at CERN is with relativity. If we view time like a river current created by mass then we could say that the “current” created by the earth overpowers the current of the small atomic antimatter we have. If I had the budget and the scientific potential I could test this. First I would observe free antimatter in a true vacuum in space and measure how it relates to entropy, because if it displays negative entropy, we could conclude in an experimental fashion that antimatter experienced time. The next test I would do was if I could get far enough away with enough antimatter that the gravity produced by the antimatter is large that the gravity of any matter felt, I would observe how the antimatter experiences time to see if it is backward. One note about this is that the antimatter would have to produce more gravity or the same gravity and me and the equipment I would bring. This would replicate the conditions right before the big bang allowing me to see if antimatter would go back in time during the big bang, because during the big bang the matter and antimatter would be equal. One more thing to note is that once the galaxies have expanded far enough away from the milky way it may actually be possible to do this experiment, however many millions of years we are away from this time. Thus my conclusion ends up as another hypothesis, maybe antimatter experienced time and mass as a negative value.

 

References 

General knowledge (1) - Mass-energy Equation | NRC.gov:  https://www.nrc.gov/reading-rm/basic-ref/glossary/mass-energy-equation.html#:~:text=The%20equation%20developed%20by%20Albert,equal%20to%20E%2Fc2. 

More general knowledge (2) -  https://faculty.wcas.northwestern.edu/infocom/Ideas/energy.html#:~:text=A%20joule%20is%20the%20amount,%2Fs2%20%3D% 

Helped form hypothesis (3) -  https://byjus.com/question-answer/is-energy-a-vector-quantity/#:~:text=Energy%20is%20not%20a%20vector,as%20it%20has%20magnitude%20only.

Contains list of case studies (4) -  https://timeline.web.cern.ch/timeline-header/86

Even more general information (5) - https://en.m.wikipedia.org/wiki/Pion

General knowledge (kaons) (6) -  https://en.m.wikipedia.org/wiki/Kaon#:~:text=In%20particle%20physics%2C%20a%20kaon,down%20antiquark%20(or%20quark).

ATRAP magnetic moment (7) -  https://home.cern/news/press-release/cern/atrap-experiment-makes-worlds-most-precise-measurement-antiproton-magnetic

More on ATRAP magnetic moment (8) -  https://home.cern/news/press-release/cern/atrap-experiment-makes-worlds-most-precise-measurement-antiproton-magnetic

LCHb information (9) -  https://home.cern/news/press-release/cern/lhcb-experiment-observes-new-matter-antimatter-difference

More on LCHb (10) - https://home.cern/news/press-release/physics/lhcb-sees-new-flavour-matter-antimatter-asymmetry

Even more on LCHb (11) -  https://lhcb-outreach.web.cern.ch/2013/04/24/first-observation-of-cp-violation-in-the-decays-of-b0s-mesons/

ALPHA charge information (12) -  https://alpha.web.cern.ch/publications/experimental-limit-charge-antihydrogen

Cronin and Finch information (13) -  https://timeline.web.cern.ch/cronin-and-fitch-detect-difference-between-matter-and-antimatter

More on Cronin and Finch (14) - https://arxiv.org/pdf/1304.6173.pdf

ASACUSA mass information (15) -  https://home.cern/news/press-release/cern/cern-experiment-improves-precision-antiproton-mass-measurement-new

ALPHA-G information (16) - https://www.nature.com/articles/d41586-023-03043-0

ALPHA and light (17) -  https://home.cern/news/press-release/cern/alpha-experiment-observes-light-spectrum-antimatter-first-time

CP violations (18) - https://en.wikipedia.org/wiki/CPT_symmetry 

All of the particle physics information (19) -  I.S. Hughes, Elementary Particles, Cambridge University Press, Cambridge, 1985.

Acknowledgements 

 

There are a lot of people that I would like to acknowledge. My parents, my dad robert and my mother sharon, who helped me edit and come up with ideas. I would also like to thank some of my greatist science and math teachers through out the year. they are, Mr.barker my grade 6 sci and math teacher, Ms.webb, my grade 7 sci teacher, Mr.arnott, my grade 9 sci and math teacher, Ms.chung, my grade 10 math teacher, Ms.sheehan, my grade 10 sci teacher, Mr.Penny, my grade 10 physics teacher and Mr.Johnson, my grade 10 math and sci teacher.