Conclusion:

• Thus, assuming that dark matter is made of neutralinos we may be able to harness its explosive properties to convert it to energy so we can power spacecrafts

Next Question:

• How does Dark Energy affect things differently from normal energy and dark matter?

• General relativity works well to describe events that took place following the beginning of the universe, but falls flat when trying to explain its birth. The Big Bang’s singularity would have infinite density (causing infinite curvature of space), which isn’t possible - at least according to general relativity.

• Therefore, theories of quantum mechanics are also required to sufficiently explain the beginning of the universe. Two of the prevailing theories are as follows:

The “no boundary” proposal

• Attempts to explain how the universe expanded at the very beginning of its life while avoiding the singularity that broke general relativity

• The theory path uses integrals to perform calculations in quantum theory. These path integrals essentially find the probability of an event by performing a sum over all ways that event could have occurred

• By using this math, Stephen Hawking and James Hartle hypothesized the initial expansion of the universe

• According to the creators of this proposal, the universe started with no size, but expanded smoothly - without a singularity in the first place.

• This removes the initial singularity and clears up the original issue with general relativity’s explanation of the universe’s genesis
  

The tunneling proposal

• Unlike the no boundary proposal, this theory attempts to rationalize the initial singularity with quantum tunneling instead of removing it

• According to this theory, the singularity has zero size but finite density. This is a state that, according to classical physics, cannot happen

• Luckily, quantum tunneling allows particles to do things deemed impossible by classical physics

• According to this proposal, the universe could have started with zero size but finite density thanks to a quantum tunneling event

Next question: How does quantum tunneling occur in the first place?

Next question: What are the practical applications of quantum tunneling, and how do scientists utilize this phenomenon in technology and research?

Schrodinger equation

• The behaviour of particles in a particular space and time is shown through the Schrodinger equation using waves for material particles

• This equation helped to explain quantum tunnelling

• The Schrodinger equation provides qualitative reports to understand quantum tunnelling and is crucial for figures of tunnelling which are advanced

• Quantum tunneling can also be explained using The Uncertainty Principle

The Uncertainty Principle

• This principle claims pairs of properties in particles like position/momentum or energy/time are not able to be known at the same time.

• It also states that measuring conjugated variables simultaneously cannot be done with complete accuracy

• The higher accuracy is known for the momentum of a particle, the less certain the position is and vice versa

• Thus, tunnelling takes place when uncertainties of momentum and kinetic energy in a particle are big enough to surpass the energy barrier

• This phenomenon can be understood using various wave-particle dualism interpretation

  
  

Conclusion

• There are multiple ways to find out how quantum tunnelling occurs with The Uncertainty Principle and Schrodinger Equation using wave-particle dualism. Using The Uncertainty Principle, however, we know that tunnelling happens if the uncertainty of momentum and kinetic energy is large enough to surpass the energy barrier

Next Question:

• What concepts in quantum physics challenge our understanding of how physics generally works and how do they do so?

Next Question:

What are the limitations of using dark matter as rocket fuel? Could there be limitations with mixing with normal matter?

Dark Matter

• The formation of galaxies since the big bang wouldn’t have been possible with only gravity from visible matter

• In the 1930s, the existence of dark matter was first observed and they have since been predicted to make up 85% of the universe

• Dark matter is believed to consist of particles similar to neutrinos and don’t have much interaction with visible matter

Dark Energy

• Dark energy was discovered in 1998, following the discovery of the acceleration of the expansion of the universe

• The presence of dark energy was not obvious earlier in time because the original energy from the big bang was the cause of most of the universe’s expansion

• Dark energy has a constant density as the universe expands, meaning is continues to create energy as the energy is scattered throughout more space

• The current models which we are basing predictions and observations on are based on Einstein’s theory of general relativity, so future discoveries on the existence of dark energy (or rather its lack of presence) could prove this theory wrong

What new technology is being made to learn more about dark energy? How is it different from the current technology and telescopes being used?

• Dark energy is a hypothetical reason for why the universe is expanding at such a fast rate and is thought to work similarly to "anti-gravity". This means rather than pulling objects closer together, it stretches them apart and expands the fabric of the universe

• Dark energy is between 68% and 72% of the universe's mass and energy and doesn't seem to affect galaxies and stars, other than physically drawing objects apart from one another

• An object 100 million light years away will be traveling 21500 km/second away, this rate increases significantly as objects are farther and farther away 

• Interestingly enough, Gravity acts stronger on objects than dark energy at a smaller scale

• Galaxies and stars do not become thinner as the distance between them expands because of dark matter

Dark Matter

• What is dark matter? Candidates for what it can be are: a fifth force that causes negative pressure which expands the universe, particles that instantly come in and out of existence, and a vacuum energy 

• We don't know what dark matter is, we can only make guesses based on what its effects are on the universe 

• Without dark matter, most believe the universe would have imploded as large galaxies would grow closer to one another 

Next Question:

How might Dark Matter and Dark Energy be connected? What are we currently doing to better our understanding of what Dark Energy is and come to a solid conclusion?

• Artificial Intelligence (AI) allowed them to study dark energy with greater precision and efficiency than traditional methods of research while having less data 

• Created a supercomputer simulation of the universe using ratios of dark matter to regular matter to understand how dark energy influences the universe 

• AI was employed to showcase the effects of dark energy in the past 7 billion years on a specific area of the universe by creating a map

• Using AI makes finding observations and conclusions quicker, often drawing our attention to patterns within data we regularly would not notice

• This AI map created represented data for 100 million galaxies, something that would require a ton of data (

• The map was then used to better align cosmic evolution models according to dark energy dynamics 

• This project would require 4 times as much data to be executed with as much accurateness
  

Researchers at ETH Zurich (Other Article)

• Used Machine Learning models that use facial recognition to estimate the amount of dark matter there is in a particular location of the universe. This is done by looking for "signs of dark matter".

• Dark matter is invisible to telescopes, however, it bends light rays, distorting images of galaxies. This and the mass of the sky are used to build maps and compare to predictions previously made regarding how much dark matter is present.

• Maps are then related to one another and AI is used to find patterns among the maps.

• Deep neural networks are then used to extract as much information as possible and optimize for “dark energy signs” to make maps as accurate as possible.

Question:

How are scientists ensuring that the technology we use to research Dark Energy is accurate? As we do not have any solid theory concerning dark energy and are currently in the early stages of using Machine Learning in astrophysics, how do we measure the accuracy of our conclusions?

Question: How do quantum computers utilize quantum tunneling to perform computational tasks, and what advantages does this offer over classical computing?

• In classical physics, objects must be particles or waves. In quantum physics, however, objects are neither

• Unlike in classical physics, it is essentially impossible to predict actions in the quantum realm

• Thus, the trajectory of a quantum object can no longer by found using normal physics equations, but instead using the Schrodinger equation

• In quantum physics, every measurement is random and probabilistic to some degree

In addition to this, quantum objects have a number of properties that would be impossible according to classical physics:

Quantum Entanglement:

• Two quantum particles become “tangled”, gaining the ability to transfer information between them

• This information transfer doesn’t happen through communication, however. The two particles essentially act as the same object, existing in two places at the same time

Quantum Tunneling

• A quantum particle performs an action without the energy required to perform it

• For example: a quantum physics ball could (with a small chance) roll through a hill without the energy required to push it over, whereas a classical physics ball would never reach the other side.

• This violates the classical law of energy conservation

Next Question: What were the earliest experiments that led to the discovery of quantum mechanics?

The longer answer:

Despite sharing similar names, dark matter and dark energy are not connected besides their shared invisibility and difficulty in observation.

Dark matter is, well, matter. It is responsible for the much of the mass of the universe at large and helps keep galaxies organized. Due to its mass, it increases forces of gravity at a universal scale, drawing the universe closer together and slowing its expansion.

So, with all these forces keeping the universe together, how is its expansion accelerating?

Interestingly, this is where dark energy comes in. Not only is it a different type of thing altogether (energy, not matter), but it actually has the opposite effect on the universe. In addition to this, dark energy is a lot stronger and more prevalent, making up about 68 percent of the energy that exists. Overpowering the force of gravity and dark matter, it pushes objects apart and expands the universe. 

In conclusion: Despite their similar names, dark matter and dark energy are actually comically different. One is matter, one is energy. One vastly overshadows the other in prevalence in power. And, of course, they exert completely opposite forces on the universe!

Next Question: Will dark energy continue to accelerate the expansion of the universe forever? Will it eventually slow down, stop, or even reverse? What would happen to the universe in these cases?

• Quantum tunneling is a phenomenon which breaks the rules of classical mechanics, involving the penetration of potential energy barriers

• Subatomic particles are found on the other side of physical obstacles, able to reconnect there

• Transmission through a barrier is dependent on the barrier’s height and width, only able to have a thickness of 1-3 nm

• Because of the uncertainty regarding the exact location of an electromagnetic particle, they are able to dey the laws of classical physics

Applications

• Scanning Tunneling Microscope: allows view at atomic level by using a conductor tip at the surface of the object

• Nuclear Fusion: the temperature at the centre of the site of fusion is not enough to pass the Coulomb barrier and carry out the reaction. The use of tunneling increases the probability of the particles getting through the barrier

• Quantum Biology: tunneling plays a key part in many biochemical processes such as, photosynthesis, cell respiration, and DNA mutation

Next Question:

How has quantum tunneling changed our knowledge of classical mechanics? What further development is being studied on the use of tunneling?

• Edwin Hubble was the first to observe distant galaxies in the 1920s and discovered that the Universe was expanding

• Afterwards, in 1988 studies showed that galaxies began a phase of accelerating expansion

• The source of this expansion was referred to as “dark energy” which acts as the opposite of gravity, repulsing things from it

• Dark energy suppresses the merging of large cosmic objects which would’ve formed because of gravity

New data

• Later on, the Max Planck Institute used the eROSITA X-ray space telescope in 2019 to check galaxy clusters

• The telescope found approximately 500 galaxy clusters, making it one of the biggest cluster samples in the past 10 billion years

• Researchers I-Non Chiu (from National Cheng Kung University, Taiwan), Matthias Klein, Sebastian Bocquet and Joe Mohr (from Loyola Marymount University, USA) teamed up to use the data formerly mentioned and others from across the globe to characterize the galaxy clusters

• The researchers also measured the masses using gravitational lensing

• The first cosmological study of dark energy using galaxy clusters was done thanks to combining the data

Calculations and Theories Using the New Data

• It was discovered that 76% of the total energy density in the Universe was made of dark energy when comparing all the datasets and predictions

• Calculations have been done to point out that dark energy remains uniform in space and constant in time using its energy density

• Using all this observational evidence, it is suggested that dark energy is described as a cosmological constant

Next Question:

• How can we visualize/model what dark matter or dark energy is? How does this help our understanding?

• Robert McGehee, Aaron Pierce and Gilly Elor, researchers at the University of Michigan (USA) and University of Mainz (Germany) have a new model for Dark Matter called HYPER

• HYPER stands for HighlY interactive ParticlE Relics

• The HYPER model believes that in the initial stages of the universe, after dark matter was formed, the interactions of dark matter and normal matter were at a sudden increase in strength

• This idea allows for not only the possibility of dark matter to be detectable today but also explains all of the dark matter scattered throughout the universe

• Physicists have been looking for heavy dark matter particles (WIMPS), however, they’ve been unsuccessful which led to a pivot onto lighter alternative dark matter particles

• The HYPER model has been the closest we’ve been to picturing a phase transition which helps make dark matter easier to detect

• The usual problem with other models is dark matter and normal matter interacting with each other too strongly, because then what’s formed is too minuscule, contradicting astrophysical observations

• On the other hand, if the amount formed is the exact perfect amount, the interaction would be too weak to detect with the experiments being done

How it works

• Interactions with dark matter and normal have been facilitated using a certain particle (mediator)

• The interaction depends on the weight of the mass; the dark matter and its detection using this mediator is dependent on it

• It is essential the mediator is initially heavy so the right sample of dark matter is made and then turned lighter to continue the detection of the dark matter

• This process requires the mediator to have a phase transition right after the dark matter is formed

Next Question:

• What have models of dark matter and/or dark energy led to in terms of discoveries, concepts and perspectives?

• Scientists have not found a certain answer to what will happen to the universe, however there are some theories

• If the universe continues as it is, the universe and everything in it will eventually go cold and die out since no new stars will form

• The strength of dark energy could possibly change as well and accelerate even more, causing speeds which will cause the universe to tear itself apart

• Both these possibilities would mean the universe will continue to expand infinitely

• There is a possibility that dark energy works very different than we imagine, resulting in the slowing down of the universe’s expansion and eventual halt, starting to recompress, and then re expanding

Next Question:

How is the Hubble Constant being calculated? What may be the areas of fault in these calculations causing Hubble Tension? How are we continuing to research?

• In the 1920’s, Edwin Hubble used his experience with telescopes to make measurements of Cepheid variable stars (stars that vary in diameter and temperature)

• These measurements were used to calculate their distance from Earth, but also allowed the discovery that distant stars were moving away faster than ones nearby.

• Using this new observation, Hubble and Milton Humason calculated the relationship between the distance to a star and the speed that it is moving away from our planet - this is the Hubble constant!

• The original estimate was 500km/s/Mpc, much higher than what it is agreed to be today

• Through improvements on Hubble’s methods, the more accurate Hubble constant was determined to be about 70/km/s/Mpc

• Even still, different methods for measuring this constant disagree with one another, so science still has a long way to go

Measuring the Hubble Constant

• To find the Hubble constant, scientists must find the distance to an object in space, as well as how fast it is moving from the observer

• Using the Doppler effect, scientists can find the velocity of the object relatively easily

  • Similar to its effect on sound, the Doppler effect stretches light, increasing its wavelength and “redshifting” it

• Astronomers can measure how much the light shifted and use it to find how fast the object is traveling away from the observer

• The main source of inaccuracy is the distance between Earth and an object, which is much harder to measure

• Many methods have been used to find this distance, each giving different results (This is Hubble Tension!)

• Some methods include:

  • Comparing the brightness of an object to how bright it looks from Earth

  • Analyzing the strength of gravitational waves

  • Modeling the cosmic microwave background radiation

As technology continues to advance, astronomers will continue to inch closer to the true value of the Hubble constant. Some are working on a new generation of telescopes, others continue to refine their analysis of gravitational waves - our understanding of this Hubble value will be in constant evolution.

Next Question: What other applications exist for the Doppler effect as it "redshifts" light (or other things)? Does it allow us to learn anything else about our universe?

• Quantum Tunneling (part of quantum mechanics) does not align with classical physics mainly because particles can exist by going through barriers even if they cannot go over barriers. This is because particles can exist in more than one place at the same time 

• The thinner and shorter the barrier, the higher the probability of the particle going through the barrier 

• An external electrical field or reducing the temperature helps in the tunneling process. Lowering the temperature means particles need less thermal/activation energy

• Tunneling can also help in catalyzing reactions through enzymes or be used to make semiconductor walls thinner, in order to transfer electrons faster and easily

Classical Mechanics Limits of Quantum Tunneling: 

• Particles will take the path of least resistance through a barrier, but this is not true for quantum particles 

• Energy conservation does not apply to quantum particles as it does in classical mechanics. This is because particles do not have defined trajectories, rather they exist in multiple states at once 

• Analogy: (Classical Mechanics) The Ball rolls uphill and comes back down if it does not have enough energy to overcome the hill vs (Quantum Mechanics) The Ball will tunnel through the hill and make it to the other side

• The ball exists on both sides of the barrier with a specific probability of being on each side even if it does not have enough energy to overcome

The Quantum Viewpoint: 

• It may seem counterintuitive to tunnel through a barrier for a particle that already doesn't have enough energy to overcome a barrier. This is why we have to understand the probabilistic nature of the quantum viewpoint (particles have superpositions and don't have to be either on one side or the other) 

• Heisenberg Uncertainty Principle: We do not know both the position and momentum of a particle accurately at the same time, it is always somewhat uncertain. That is why we can also consider the circumstance that the particle has passed through the barrier 

• The Wave-Particle duality concept: particles also have wave-like behavior and can tunnel through the barrier by diffracting around it, this is crucial as depending on how we observe and measure a particle, it can be acting like a particle or acting like a wave

• Particles will take an infinite amount of time to overcome an infinitely expanding barrier, however, there is a finite amount of time a particle will take to tunnel through a barrier, this allows us to explore the concept of tunneling time

Next Question: How can we use Quantum Tunneling to predict/model the probability of an ultimate fate of the universe such as the Big Crunch or Big Freeze?

3 scenarios:

• The universe collapses because gravitational attractive force overcomes the expansion of the universe 

• Expansion overcomes gravitation and ends in a Big Freeze

  • Expansion of the universe and gravitation balance out as the universe never collapses but expansions are ceased

Dark Energy as a Constant

• Measuring the shift in light that travels from galaxies can help us measure the change in expansion 

• Galaxies observed in the 1990s were seen as receding rapidly and then eventually slowing down. Based on this information, it was predicted that we could tell if the universe would collapse based on how the slowdown of the recession speed

• However, through the collection of data from observing many galaxies, scientists found that galaxies were not receding at a slower rate but were instead receding at a faster rate away from us

• ^ This is where dark energy, another component of the universe was conceptualized. Based on the current data collected, many believe that dark energy is a constant because there is no change in its energy density.

• Based on the theory that dark energy is constant, this will also mean that as the universe expands, and its volume increases, there is more energy in the universe. 

• Structures in the grand scheme of things will expand further apart, yet the Local Groups and Milky Way will remain the same as they were previously bound together through gravity. Eventually, the Milky Way and Local Groups will look like one giant galaxy as the universe expands. With consideration to this information and experiment, there is a possibility that the universe will end up in a Big Freeze (heat death where the universe has no thermodynamics and can no longer sustain entropy)

Next Questions:

• What are the possible ultimate fates of the universe if Dark Energy is not a constant, but rather changes with the expansion of the universe?

• Are current experiments being conducted on the signs of Dark Energy and whether it is constant or not?

• What leads scientists to believe that dark energy is constant, despite this invalidating the Law of Conservation of Energy?

1. Qubits and Superposition: Quantum computers use qubits as their basic units of information, which can exist in superposition, representing both 0 and 1 simultaneously. Quantum tunneling allows qubits to explore multiple computational paths simultaneously, thanks to superposition.

2. Quantum Gates and Algorithms: Quantum gates manipulate qubits, similar to classical logic gates, but exploit quantum properties like tunneling. Quantum algorithms, such as Shor's algorithm and Grover's algorithm, utilize quantum tunneling to solve certain problems much faster than classical algorithms.

3. Exponential Speedup: Quantum computers offer the potential for exponential speedups over classical computers for specific tasks. This is because quantum algorithms can leverage quantum tunneling and other quantum phenomena to process information in parallel, exploring a vast solution space simultaneously.

4. Quantum Annealing: Quantum annealers, a type of quantum computing architecture, utilize quantum tunneling to optimize solutions to optimization problems. By encoding the problem into the configuration of qubits and controlling the system's parameters, quantum annealers exploit quantum tunneling to find optimal solutions efficiently.

Quantum tunneling enables quantum computers to perform computations in a fundamentally different way from classical computers, offering the potential for significant speedups and breakthroughs in various fields of science and technology.

Next question: What are some of the challenges and limitations facing the practical implementation of quantum computers, and how are researchers addressing them?