#physics friday

[oliviax727]

Physics Friday: WTF is Dark Energy/Dark Matter? (Part 1)

To see what this is all about click here.

Preamble: Dark Numbers

Education level: High School (Y9/10)

Topic: Cosmology (Astronomy)

This equation is surprisingly the best representation of what we are doing with dark energy and dark matter. The equations we are using to figure out the nature of the universe are quite literally 'not adding up'.

When we have a situation where we encounter a missing number we are faced with three scenarioes:

Our model is wrong and we fucked up, physics is over

Our model works, but it's not complete. There are situations where it doesn't apply, and we are seeing an example of it

Our model is simply missing a few terms

Scenario 1 would imply that basic physics such as Newton's laws of motion and gravity are just plain wrong. Which is ... well ... a bit difficult to try and prove.

Scenario 2 implies that there is a more fundamental theory that underlies our current one. While it is not off the table, it can be difficult to find a theory for just one or two specific phenomena.

Scenario 3 is like 2, but it's a bit 'softer', what we're doing is just adding an extra number to balance out the equation and then trying to answer "What does this number mean"?

By Occam's razor, we can go with option 3, as it's simpler, and also appears to be more correct than a complete model change.

Dark Matter and Galaxies

Our galaxy is like the solar system in the sense that there is a large object in the centre surrounded by a bunch of stuff moving around that centre.

The difference between the two is the ratio between the central mass and the mass of the rest of the system.

If you combined all of the planets in the solar system together, it would still be less massive than the Sun.

This means we can easily calculate how the planets move around the Sun. As the motions of the other planets don't really affect that motion all too much. And thus we can use Kepler's 3rd Law:

If you combined all of the stars in the galactic 'orb' surrounding the centre, you find that it would be much heavier than the black hole in the centre.

This means you have to account for a more spread out mass as you change your distance from the centre of the galaxy.

The further you are from the centre of the galaxy, the more stuff there is beneath you i.e. there's more stuff closer to the core than you. We have to calculate gravity taking this mass, and the radius to it, into account.

Thankfully, we have methods that can calculate this much easier. And we can use this to figure out our orbital velocity as a function of distance from the centre.

So let's try and calculate things! Take a galaxy, measure it's mass distribution independent of orbital mechanics, and find the orbital velocity!

Image Credit: Citizendium

What we get is the graph above. In a normal universe, we expect our orbital velocity to increase near the core as more stuff gets added to the mass pulling us in. It then peters out as gravity looses it's strength.

What we actually see is that the orbital velocity takes a lot longer to peter out. If Newton's Laws/General Relativity are working how they should, this means that there must be a lot more mass in the galaxy.

What's worse is that this mass is much more evenly distributed. And not just that, but we cannot see it i.e. it does not interact with electromagnetic waves (light).

Hence we label this weird matter 'dark', because we can't see it and it helps us account for the disparity in the equation.

Next time I'll go into what we think dark matter actually is.

Dark Energy and Einstein's Blunder

General Relativity is one of the most backed-up theories in all of physics. The original conception of the theory comes from the Einstein Field Equations (EFEs):

We can safely ignore all of the fancy jargon symbols. What's important to us is what's missing.

When Einstein was playing around with his equations, he made an error. This error led him to missing a part in his equation. And thus he added an additional term to the EFEs:

This capital lambda term (Λ) helped balance his erronious equation.

Eventually, Einstein figured out that this was a mistake, a mistake so big that he called it his 'Biggest Blunder'. It turns out that the EFEs don't require Λ to actually work.

A few decades later, in the 1990s, researchers were trying to use the principles of general relativity to figure out the expansion of spacetime. Thanks to Edwin Hubble, we knew that space was expanding, but we didn't know how it was expanding.

The difficulty is that both the curvature and the amount of energy in the universe affected the expansion of the universe. This is dictated by the Friedmann equations:

Where the a's are the universe's scale factor, i.e. the current 'size' of the universe. The two p's are the mass and energy densities in the universe.

Using measurements of Type Ia Supernovae (you will see a topic on this in the future as I've done research into this), two teams of researchers were able to determine that the expansion rate of the universe was accelerating! Something completely unexpected.

This would require us adding an additional term to the equation involving our suspicious little friend:

This Λ variable, called the cosmological constant, can be propagated up the mathematical derivation chain to show that Einstein's 'mistake' was actually the correct equation all along!

The cosmological constant acts a energy density term that exists outside of our current understandings of the matter and energy in our universe. And because it's outside of our understanding, we call it 'dark' energy - because, just like dark matter, we can't see it.

It's a type of energy that isn't represented by any of the fundamental forces. What's more is that it is constant, which means as the universe expands, more gets added. And even more is that this energy density is negative, suggesting even that the universe is not a vaccum.

This discovery landed three researchers from both teams the Nobel prize in physics. One of the laureates includes the vice chancellor of my very own university, Brian Schmidt. Doxxing myself aside, this is a fact that neither me, nor my university, will shut up about.

In another part, I'll talk about what this dark energy could be and what an accelerating expansion of the universe could mean.

Conclusion

So despite the names, dark energy and dark matter are actually two different things that have two different sets of properties purposes (at least that's what we think). The names simply derive from the same method of using constants to help make our equations work better with reality.

It's always possible that we are wrong and there is a more fundamental equation that helps us understand these things. But that's a task for the future.

Hope you enjoyed reading and please give me feedback! I'm doing this every week as well, so feel free to follow if you want.

Next week I'll probably do something mathematics-related, before continuing on with this part.

[oliviabutsmart]

Physics Friday #12: Interpreting Quantum Mechanics

Preamble: "God does not play dice"

Education Level: High School (Y9/10)

Topic: Quantum Mechanics (Physics)

Developing the Schrödinger Equation

Quantum mechanics had it's origin in the nature of light, and then over the course of 50 years from 1900 - 1950, the entire field of physics was overturned as we realised that waves weren't just limited to light, but everything.

This came to it's head in 1926 with the creation of the Schrödinger wave equation, which dictated how particle 'waves' evolve in time and space.

Now you've probably heard of the wavefunction. Effectively, it's a probability wave, where the amplitude of the wave corresponds to the most likely location you'd find the particle.

The wavefunction doesn't just involve a probability distribution in space, but also in other quantities.

For example, if you put an electron in a small box, you can imbue it with an energy.

But because of quantum mechanics, energy is quantised - there is an energy of X joules, 2X joules, 3X joules, etc. If you put an electron of 2.5X into the system it can't just work like that.

Which is why the electron forms a weighted combination of different states corresponding to specific multiples of our X value. And this superposition just so happens to be the average energy, which is considered the classical energy of the electron.

For example an electron with a superposition of 2X, 50% of the time, and being in state 3X 50% of the time. This averages out to 2.5X.

Collapsing the Wavefunction

But how do you find a particle? Or measure it's energy? Well, via what's known as the wavefunction collapse. When we take a look at the particle as a wave, it suddenly snaps to a specific value and then evolves from there.

This wavefunction collapse can occur for any observable property of the particle. If you measure the energy of our 2.5X particle in our above state, it's a 50/50 chance that you'll catch it in either state.

And once the coin flip occurs, the particle's energy will suddenly jump to 3X or 2X and remain at that value.

You may think this violates the conservation of energy, but remember that the act of 'measurement' intrinsically involves interacting with the electron - a very important point.

But wait, what does this collapse mean?

The Schrödinger equation does not explicitly mention this collapse. It simply describes the evolution of an undisturbed wavefunction. Thus, we need to include collapse as a part of the three postulates of QM:

Particle states are described by a wavefunction, a vector belonging to a Hilbert space

The Schrödinger equation dictates the time evolution of these states

Measurement of an observable (i.e. a hermitian operator) collapses the wavefunction to an observable's eigenstate (each eigenstate being associated with a probability of collapse)

But this still doesn't really answer the question. What is measurement? What counts as measuring an observable property of the particle?

Well here's the thing ... we don't have an answer ... it's an open question and the topic of this post.

The interpretations

An interpretation of quantum mechanics is effectively a theory that aims to answer this question: where and how does this measurement occur?

After almost a century since the formulation of standard QM, we have a litany of many interpretations, most of which fall on a spectrum of when exactly it occurs.

On one end, we have ideas where the wavefunction never existed in the first place, or that the wavefunction naturally collapses.

On the other, we have ideas that the wavefunction collapses at a point very far in the process, or even that it never collapses at all.

I'll talk about 6 of these interpretations, although some of these theories of collapse are more categories of theories.

Think of the Ocean (Pilot Wave)

In the 1920s, de Broglie developed an interpretation of quantum mechanics that posited that subatomic particles do, in fact, physically exist.

The source of the wavefunction and the probabilistic nature of quantum mechanics is caused by the particles being guided by a series of "pilot waves" - which push and move the particles around and imbue them with the motion and energy we observe.

The randomness comes from the fact that the waves themselves depend on the positions of all particles. These guiding waves are dictated by a special guiding equation.

dear lord that's complicated Image Credit: Wikipedia

This guiding equation, when applied to particles just so happen to result in our neat and clean Schrödinger equaiton.

So what happened to this theory?

The biggest problem with this theory is that it's non-local, meaning that the evolution of the guiding wave requires knowledge of all of the particles in the universe.

This of course, violates special relativity.

Another problem is that it lost the authors' support, or that the authors lost support. de Broglie rejected the theory in 1927 and David Bohm, the other author, was distanced from the other scientists for being outwardly socialist during the early red scares.

Pilot wave theory, in a sense, is so strict on the physicality of particles that it ends up sort-of wrapping around and becoming a many-worlds theory instead, to quote David Deustch:

Pilot-wave theories are parallel-universe theories in a state of chronic denial.

This arises from the problem of branching, a tacked-on attempt to reconcile the nature of the theory. That since the wavefunction was a physical thing, and the pilot wave and particles kept self-interacting, it sort of creates branching realities caused by distant communication with other particles.

Those silly numbers are hiding from us! (Hidden Variables)

The EPR (Einstein-Podolski-Rosen) paradox is another famous problem in QM, caused by entanglement.

Take two electrons and force them to collide with eachother, bounce off, and travel far into the distance. We know that after the interaction, these electrons propagate with free-particle wavefunctions. And we can fire them at eachother such that we don't know their momentums initially - i.e. they entangled.

Now wait for the electrons to travel very far away from eachother, and then measure one of the electrons momenta. In order to maintain conservation of energy, we instantly know what the momenta of the other electron is.

What we also know is that because of this measurement, and that the electron is entangled with the other, that we have just collapsed the other wavefunction instantaneously from a distance.

This is a problem, due to special relativity, we cannot transfer information faster than the speed of light. So clearly our QM is broken.

Hidden variable theories aim to solve the EPR paradox as well as just generally trying to interpret quantum mechanics. Effectively, there are a series of unobservable entities that dictate how wavefunctions collapse.

The wavefunction in the EPR paradox has a hidden variable stating the electrons' momenta so that we aren't violating causality, for example.

Fortunately, but unfortunately, this theory makes a testable prediction via Bell's theorem, which utilises entanglement to determine if these hidden variables work locally.

The experiments conducted show that only a non-local hidden variable theory is possible. One example of this just so happens to be our previous pilot-wave theory!

Observing isn't needed (Spontaneous Collapse)

We could be thinking of this wrong. Perhaps the wavefunction is real, and it is non-deterministic. But that at some point, it collapses on it's own.

There are several ways to do this, but at it's core, these are how the theories go:

There is an extra non-linear term in the Schrödinger equation, that is insignificant at the small scales

This non-linearity causes the wavefunction to be unstable, and prefers it to collapse to observable eigenvalues

With increasing complexity, this term becomes much more important, as more entanglement = more instability

The rate of decay increases as you entangle the system. And if a system is large enough, it's likely to collapse into a classical environment

Effectively, they say that the wavefunction will collapse on their own. And the reason we don't see it on larger scales, or see a collapse when measuring the system, is that the act of interaction (entanglement) causes the wavefunction to be more likely to collapse.

Of course, the theory has trouble reconciling with relativity. As entanglement works over large distances. Models can be made to try and say that entanglement over these distances increases instability for example, but we're still waiting on developments.

Lastly, we have the problem of tails. The wavefunction of a particle exists for all of physical space. At these far out distances, it is very possible for particles to get entangled with distant objects. Meaning that a wavefunction may end up collapsing further than we think.

The easy way out (Copenhagen)

The Copenhagen interpretation was developed in the 20s to attempt to come up with some placeholder answer to what collapse is. It is our middle-of-the-road theory which states that observation of an observable causes collapse.

Observation is defined as the act of applying an observable operator (like the energy operator) to the wavefunction by an external source to gain information on that operator's outcome.

The problem is that this is a meaningless statement. Because anytime a system entangles itself with something greater, it technically does this 'observation'.

Take the double split experiment.

Image Credit: Discovery Channel

What defines the moment of observation? Is it when:

The particles interact with the measuring laser

The measuring laser interacts with the larger observation device

An electronic signal is sent from the device to a computer

The light from the computer interacts with the conscious observer

We can't pinpoint the specific cut-off between the quantum world and the classical.

After all, we know that lasers can entangle themselves with atoms. And that electronic signals are nothing but moving electrons.

The point of the theory is that it's a placeholder. The definitions are ill-defined because we're kinda waiting for another theory to help us.

It's all in your head! (Consciousness)

The immediate answer to the Copenhagen interpretation could be that the collapse occurs at the end of the specified chain. When a conscious observer interacts with the entangled system.

It's a nice idea given that it kills two birds with one stone - it helps point to a physical theory on the nature of sentience, but also allows us to solve the measurement problem.

This does come into conflict with our current understanding of sentience. Our placeholder theorem is effectively that conscious experience is an emergent property of a series of interacting electrical signals in our brain.

This placeholder helps explain why humans are more 'sentient' than animals, or very young children, as we have a very active and complex central nervous system.

Of course, it's just a placeholder. We don't have an actual meaningful answer to sentience, and probably won't for a while. So for now it's left to the dark realm of god of the gaps.

Where it comes into conflict with QM is that a series of interacting electrical signals sounds exactly like an entangled system. So there clearly can't be just emergent properties involved otherwise we're just dealing with a spontaneous collapse theory.

There has to be something physically unique about a sentient brain to cause the collapse - effectively you require the existence of a soul. Something which is even further in the dark realms of philosophy.

Another issue is that it doesn't work with special relativity, as it violates the EPR paradox still.

We also need to determine what counts as sentient. Sentience isn't an on and off switch. There are many ways it can be expressed.

We know that some mammals have some form of conscious experience - so then are cats capable of collapsing the wavefunction?

Finally, what about the universe prior to consciousness? Did it just end up in an entangled nightmare until somehow we got an observer to collapse it all? How can something built of entangled particles end up collapsing itself at some given size?

This interpretation is very interesting, however if it turns out to be true, we'll be stuck with our measurement problem for quite a while.

For now, the biggest problem with the interpretation is that it opens the door to many, many quacks like Deepak Chopra. Who think that we can control this collapse with our minds and alter our reality by just thinking it away WoOOoOoWwowoWoOo!

Forever entangled (Many Worlds)

So, assuming that our consciousness theory is not the right answer, then what causes the collapse?

We can keep getting bigger and bigger:

The electrons in the double slit entangles with the laser photons entangles with the measurement device entangles with the electrical signals entangles with the computer entangles with the observer entangles with the room their in entangles with the Earth entangles with the solar system entangles with the galaxy ...

This out-spiralling entanglement continues without bound until the entire universe is in a superposition of states. And every time an interaction occurs we ourselves are being pulled into a new wavefunction.

This entanglement would've happened early, at about the time of cosmic inflation. But every new quantum event comes with a new set of entanglements.

This leads to the name Many Worlds, as we're creating new realities with every event.

Now it's important to note something important: this is not a multiverse theory. Multiverse theory is proposed source for cosmic inflation. Here, there is still one single universe. Much like how an electron in superposition isn't multiple actual electrons. The universe is just being treated as an electron.

This theory sounds far-fetched. Arguably the fact that it's unfalsifiable makes it not a good interpretation of QM. However, it is a lot simpler than the previous consciousness interpretation - it simply removes the need for a measurement process.

This satisfies Occam's razor as well. It doesn't require a mathematical formalism because the point of the theory is that the formalism doesn't exist.

However, not having a formalism makes it quite difficult to prove. It only seems to be correct in the sense that it doesn't necessarily say that measurement cannot happen, just that it's not measurement. It's entanglement.

Conclusion

Interestingly, the theories on the "wavefunction collapses early" side of the spectrum are more likely to be disproven. Primarily a consequence of the fact that they have the opportunity of making testable predictions.

Despite all of these interpretations, it's clear who stands as the best theories: spontaneous collapse and many worlds. They have their strengths, but they have fair grounding. You could argue that consciousness is also a fair contender, but it's a bit too much in the realm of fantasy - attempting to tie one big unanswered question with another.

Spontaneous collapse has proper mathematical formalism while many worlds seems to work well in an Occam's razor sense.

Regardless, that is a surface-level exploration into the many different ways we have attempted to answer the measurement problem. I hope y'all enjoyed this post and god I need to make them less long.

Please can someone fix this inverted colours issue it's like causing all of my colours on these posts to invert too thx

Reference post: https://www.tumblr.com/oliviabutsmart/732200630726377472/for-some-reason-some-reasons-only-some-images-i

Anyways, feedback appreciated, follow if want, send memes and send help.

[oliviabutsmart]

Physics Friday #14: Sound (Part 2/2)

Preamble: Let's get straight into it

Education Level: Primary School (Y5/6)

Topic: Sonic Physics (Mechanics)

The previous part 1 of my sound post is here.

Pitch and Frequency

Pitch and frequency are related to eachother, the only difference being that frequency is a physical interpretation of sound and pitch is our own mental interpretation of it.

But what exactly is frequency?

Go back to last time's example of a tick sound occurring at regular intervals ... because this sound is repeating, we can describe it's behaviour by measuring mathematical properites:

How much time passes in-between each tick (Period)

How many ticks occur every second (Frequency)

These two ideas are related to eachother, in fact Frequency is 1/Period. If you have a tick every half-second, then you can say the tick occurs twice every second.

We measure sound in Hertz, which is effectively a measure of ticks per second.

Most sounds, however, don't work this way, with repeated ticks. They act as proper waves. With zones of high pressure (peaks), and low pressure (troughs). This is where we have to introduce another variable into our equation:

The physical difference separating each peak (Wavelength)

Since these waves travel forward in the air, a detector (like our ears) will pick up the peaks and troughs as they reach our ear. We can measure frequency or period by recording the speed at which our peaks reach our ear.

But we also can relate frequency to wavelength. After all, the further apart the waves are separated, the more time it'll take for a peak to reach us after the previous one.

We quantify this relationship using c = fλ. Where c is the speed of the wave, f is the frequency, and λ is the wavelength.

Notice that we can also say cT = λ, where T is the period. This demonstrates that the physical wavelength is proportional to the amount of time between each peak.

So where does pitch come in?

As mentioned in part 1, if we continue to decrease the time between each tick, or increase the frequency, at some point we'll begin to hear a sound.

This is our brain playing a trick on us. It's like frames-per-second but for our ears. Below some fps threshold, we can see the individual pictures of a video, but above the threshold, it looks like a continuous film. Notice that fps is also another form of frequency.

When we reach this level, our brain can't distinguish between each tick and sees it as one sound. We begin to hear our first sound.

At this point, frequency becomes tied to pitch. The more rapid the ticking becomes, the higher of a pitch we hear. This is a choice that our brain makes - it's purely psychological.

Mixing different pitches

Combining different pitches allows us to create a foundation for music. In western music, our source of harmonics comes from Pythagoras, who kinda fucked it up by not using irrational numbers.

An octave is defined as a higher sound that has twice the frequency of the lower sound i.e. a ratio of 2:1. One octave above middle C (at about 262 Hz) gives us C5 (at about 524 Hz).

We can create further subdivisions like a perfect fifth, where frequencies form a 3:2 ratio. Or a perfect fourth, which has a ratio of 4:3.

Volume, Intensity, and the Inverse Square Law

Volume is directly related to the amplitude of a sound wave. Effectively, how strongly is the air being compressed at each peak?

Again, volume is just another psychological interpretation of a physical phenomena. Similar to how our eyes see brightness.

Amplitude isn't just interpreted as volume, it is also the power that the sound waves carry. Smaller amplitudes correspond to less energy contained within the moving particles.

We measure intensity logarithmically, because that's what our ears here. Effectively a wave sounds twice as loud only if the wave is 100 times as amplified. It's a similar effect to pitch, where we multiply frequencies instead of adding them.

That's where the decibel scale comes in. 1 dB = a 10x increase in the sound's power output. The decibel scale is used generally for a lot of measurements of wave/power intensity. However it just so happens that our ears behave in very similar ways.

Image credit: soundear.com

Notice that louder sounds are more likely to damage our ear. That's because when loud sounds reach our ear, it causes the inner components to vibrate. This vibration amplitude generally is proportional to the amplitude of the waves.

Too loud of a sound means that our eardrums are vibrating with too great of a physical movement. This can create tears in tissue that damage our ears' sensitivity to sound.

Sound looses power over distance

If you stand far away enough from a sound source, it sounds fainter, eventually becoming unhearable.

This is because of the inverse square law. As sound spreads out over distance, it has to emanate in the form of a sphere, going outward in every direction, in order to maintain consistency of direction.

The same amount of power gets spread thinner and thinner over the bubble that it creates. The surface area of a sphere increases to the square of it's radius.

Image Credit: Wikipedia

Thus we get a decrease in volume over time.

What the Actual Fuck is Timbre, and how do you pronounce it? (also Texture too)

Unfortunately I still don't know how to pronounce it.

Timbre is defined as the quality and the colour of the sound we hear. It also includes the texture of the sound. It's sort of the catch-all for every other phenomena of sound.

Timbre is a bit more complex of a phenomena. In that, it combines basically everything else we know about how we hear sound. So I'll go one by one and explain each component of what makes Timbre Timbre.

Interference

Wave interference is an important property that needs to be understood before we actually talk about timbre. Sound waves often can overlap eachother in physical space, normally caused by multiple sound sources being produced at different locations.

These sound sources often will create new shapes in their waveform, via interference.

Constructive interference is when the high-pressure zones of two sound waves combine to produce an even-higher-pressure zone of wave. Effectively pressure gradient add onto eachother.

Destructive interference is when a high-pressure zone overlaps with a low-pressure zone, causing the pressure to average out to baseline, or something close to the baseline.

Image Credit: Arbor Scientific (Youtube)

We can look at multiple waves acting continuously over a medium to see how their amplitudes will add up together using interference. This is the origin of more unique wave patterns.

The shape of a wave

Sound waves can come in different varieties. While the most basic shape is the sine wave. We can add different intensities, frequencies and phases of sine waves to produce more complex patterns.

I won't go into how this combination works because that's better left for a Fourier series topic. Just know that pretty much any sound can be broken down into a series of sine waves.

These patterns have a different texture, as they combine multiple different monotone sounds. Take a listen to a sawtooth wave vs a sine wave:

Warning: the sawtooth wave will sound a lot louder than the sine wave.

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This gives us a different sound texture.

Resonance

When you play a musical instrument at a particular frequency, the instrument is often resonating.

Say you produce sound within an enclosed box. Producing it at one end. Eventually the sound will reach the end of the box and bounce back from reflection (as we'll see later).

The sound will bounce back and forth, combining itself with the previous waves to produce more and more complex waveforms.

But there is a particular frequency, at which, the waves will perfectly interfere with eachother to produce what's known as a standing wave.

A standing wave will oscillate, but it will appear as if it's not moving forward. Of course, power is still moving throughout the wave, as we'll still be able to hear something.

This standing wave can only occur at a particular frequency, one in which the wave perfectly interferes with it's reflection within the box.

A standing wave (black) that is produced by two sine waves (blue and red) moving in opposite directions Image source: Wikipedia

This frequency is called the resonant frequency of the box. This frequency depends on several factors like the speed of the wave, the material inside the box, the shape of the box, and the length of the box.

The resonant frequency can be activated by our voices, as our voices or just blowing air is already a combination of different sound frequencies. The non-resonant frequencies will eventually loose all of their power as they destructively interfere, leaving only the resonant frequency, which gets amplified by what we put in

For example, you can fill a glass bottle halfway with some water, blow in it, and it will produce a particular sound. Fill it with more water, and the pitch increases - i.e. by adding the water we increase the resonant frequency.

All instruments have one or more resonant frequencies based on their material and shape (I say multiple because some instruments can me modelled as multiple boxes. Like a violin will have the inside of the wood, the wood itself, the strings, etc.).

Instruments also allow us to alter the resonant frequency by playing it differently (like putting a finger over your recorder's hole (phrasing)).

These differences in how we obtain resonance can also affect the quality of the sound.

Overtones

Resonance is not just generated with a single resonant frequency, we can create resonance with higher multiples of the the same fundamental frequency.

This is because in our box model, multiplying the fundamental frequency will allow us to create a standing wave, just with a shorter wavelength:

The A's stand for antinodes, which vibrate in the standing wave with the maximum amplitude. The N's stand for nodes, which do not move at all.

Image Credit: Macquarie University

Direct multiples of the fundamental frequency are called harmonics. Instruments can also produce other frequencies not directly harmonic depending on the structure of the 'box' they utilise.

These additional frequencies, ones which come often in fractional multiples of the fundamental are called partials. Both partials and harmonics represent the overtones of an instrument.

Overtones are what give sound additional character, as they allow instruments to not just resonate at the note they play, but at other combined frequencies. In some instruments, the overtones dominate over the fundamental - creating instruments that can play at much higher pitches.

Envelopes and Beats

Say we add two sine waves together (red and blue), each with slightly different frequencies, what we get is this:

Image Credit: HyperPhysics Concepts

We can see that the brown wave has a singular oscillation frequency, but also it's amplitude continuously scales with reference to this hidden envelope frequency, called the beat frequency (dotted line).

This difference between the actual wave's real frequency and the wave's overall frequency envelope. Is another source of timbre.

Notes, and the way we play them will often generate unique and different envelopes depending on how they are played. For example a staccato quarter-note will have a different envelope to a softly played quarter-note.

Other properties of Sound

Reflection

Different mediums mean different speeds of sounds e.g. molecules in wood (solid) are harder to move than molecules in air (gas).

These different speeds create several effects. Including the reflection of waves. Often waves require a bit of power in order to physically overcome the resistances to vibration of a particular medium.

Often this leads to sound waves bouncing back off harder-to-traverse surfaces.

Say that a sound wave travels through the air and reaches a wooden wall. The atoms vibrating in the air will hit against the wooden wall, transferring only some of their energy to the resistant wood.

The wood atoms on the border of the wall will bounce back, as expected. But this time they will transfer energy back into the air at a much greater magnitude due to newton's third law.

Thus while some of the sound wave ends up going deeper into the wood, the wood will push back and cause the air to vibrate in the opposite direction, creating a reflected wave.

Image credit: Penn State

We characterise the amount of power being reflected versus transmitted versus absorbed using portions:

A + R + T = 1

A = Power absorbed into the material (e.g. warms up the material)

R = Power reflected back

T = Power transmitted into the new medium

This is both an explainer as to why rooms are both very good, and very bad at keeping sound inside them. It really depends on the rigidity and shape of the material they are bordered by.

Refraction

Just like light, sound waves can also refract. Refraction is actually a lot simpler to understand once you already realise that waves will both reflect and transmit across medium changes.

Refraction is just combining the results of incomplete reflection (i.e. transmission) with some angle.

I won't go into refraction in too much detail, as it's worth a different topic. But effectively we experience snell's law but modified for sound.

Diffraction

Sound waves, like all waves propagate spherically (or circularly in 2D).

When travelling around corners, sound can often appear louder than if you were further away, looking at the source more directly.

This is because spherical waves will often 'curve' around corners. This is better described by light diffraction. Which is something for another time.

Conclusion

In conclusion, that's how sound works, mostly. This is a topic that is a little less closer to my expertise. Mainly because it delves into more musically-inclined phenomena that I am less familiar with. But I'm sure I did a good job.

Unfortunately, it seems like the plague of the long post is not yet over. Perhaps I need to get into a lot more specific topics to make things better for me and you (the reader).

Anyways, my exams are done. I am done. I do not have to do school anymore. Until I remember to have to get ready for my honours year (a.k.a. a mini-masters degree tacked on after your bachelor's degree).

Until next time, feel free to gib feedback. It's always appreciated. Follow if you wanna see this stuff weekly.

Cya next week where I will probably try another astronomy topic, or something like that.

[oliviabutsmart]

Physics Friday #16: The Cosmic Microwave Background (CMB)

This was originally going to be a post on Baryon Acoustic Oscillations, but I think that it's better to first discuss the CMB broadly before getting onto that, keeping the post lengths short(er).

Introduction: Our bath of Microwave Radiation

The CMB is everywhere, literally. Where you stand right now you are being bombarded by a bath of microwave radiation originating from the CMB. In fact, it's part of what causes the static on old TVs.

Now don't worry, the radiation is very weak, so it's unlikely you'll actually be hurt.

The CMB ceased to exist about 13 billion years ago, what you see in the microwave part of the spectrum is just what was left over.

Because the speed of light is not infinite, when we look really far out in the distance, we actually look back in time.

Measuring an object 1 light-year away means we only see what that object looks like a year ago. Measuring an object 1 billion light-years away means we are looking at that object 1 billion years in the past (ignoring the expansion of the universe).

If we account for an expanding universe, light actually travels a lot further. Because what was 13 billion ly has expanded into ~40 billion ly. However, we still see it as 13 billion ly.

This allows us to see the universe in it's early stages of life.

Eras of the Early Universe

The eras of our universe are crucial to understanding the CMB. In the first few seconds after the big bang, we have the hadron era, where the first protons and neutrons form.

A few minutes later, the temperature of the universe drops enought that these protons and neutrons then form into stable atomic nuclei during what's known as big bang nucleosynthesis.

Effectively we have nuclear fusion happening everywhere in space, like in the core of most stars, including our sun.

Eventually our universe expands to such a point that the temperature drops below a point where we cannot have nuclear fusion. But the temperature is still high enough that the universe is exclusively plasma.

Plasma is the state of matter in which electrons cannot bind themselves to their respective atomic nuclei, the universe is considered 'ionised' - as it's all just electricity.

During this time, the universe is opaque. Because any light moving around in the universe gets instantly absorbed by the loose electrons or nucleons.

We'll have to wait a couple thousand years before the universe cools even further, to the point where we get normal gaseous matter. The universe suddenly becomes translucent. This is known as the era of recombination.

At the moment of this occurring, any light emitted by the previously hot plasma escapes and can travel freely through the universe unobstructed. This thermal radiation comes in the form of infrared radiation.

Travelling Radiation

The radiation of the CMB is the earliest possible light we can see in the universe. Because any previously-existing light is obscured by the plasma earlier-on.

The radiation emitted from the CMB travels across space in order to reach us. And during that time it gets 'corrupted' in a sense.

Redshift - Turning Infrared into Microwaves

Redshift is a phenomena where light waves will stretch, their wavelength is increased as they are released and move through space.

Expanding space means that the CMB is effectively moving away from us at very fast speeds. This creates a doppler effect where the light waves will inherently be released out towards us at a longer wavelength. This is called doppler redshift.

The expansion of space also affects the wavelength as the photon travels. The space in-between each photon's wavelength stretches too, creating more cosmological redshift.

For most objects, cosmological redshift is negligible, because the light doesn't travel far enough for space to expand inside the wave. But the CMB is very far away, meaning that both forms of redshift are non-negligible.

Image credit: Forbes

The CMB exists at a redshift of ~1100, this doesn't mean much on it's own. What it means is that red-coloured light will become shifted to short radio frequencies that you can pick up on your radio.

The Lyman-Alpha Forest

Of course, our translucent gas is not perfectly translucent. Gas can absorb and emit specific wavelengths of light that perfectly correspond to energy levels an electron can take within an atom.

The Lyman series is an example of hydrogen emission/absorption lines, and as the light travels through hydrogen gas, the wavelengths corresponding to the Lyman series gets absorbed by our atoms.

This process keeps happening. As redshift alters the wavelengths of the surviving waves, any gas obstructing the CMB's light will have fresh light to absorb.

The effect is this continual series of absorption lines appearing in the otherwise clear spectra of radiation. Creating a 'forest' of several absorption lines.

Image Credit: Wikipedia

Re-Ionisation

Some gas in the early universe ends up converting back into plasma, this is caused by gravity pulling on small inconsistencies in the gas density.

These bright spots of plasma were what formed the first stars, galaxies, and black holes. But for us, it also effects the CMB.

Of course, ionised gas is opaque, so any light that happens to come across a star in-formation is absorbed instantly.

Observing the CMB

There have been multiple attempts to view the CMB. Despite all of our obstructions, space is mostly empty. Not just that, but the visible blemishes on our dark sky (like the milky way) can be removed in-post.

There are three notable missions: COBE (1989-93), WMAP (2001-10), and lastly the ESA Planck/BICEP mission (2015-19). Each increasing in resolution, each adding more information to our measurements.

When the CMB was first observed in the COBE mission, it saw something really strange, the CMB was really smooth, and looked like it had a dipole in it. This is the top image on the below diagram.

Image Credit: NASA

This dipole is actually caused by the orbital motion of the Earth! Not just around the sun, but also within our galaxy.

Alright, so let's try and re-configure our calculations, this time we will account for the movement of the Earth.

What we get is the middle image. There's still a big band in the centre of the frame, which actually is caused by our milky way, as the milky way itself also emits microwave radiation.

Thus this gives us the lower image. A background which looks approximately the same everywhere, but is distinctly not on local scales. This discovery broke one of our main assumptions in cosmology at the time - which is that the background is the same in all directions.

Something interesting also occurs as well. When all movement in space is removed, the CMB becomes static. This means that the CMB can act as a universal frame of reference, from which all other reference frames can be compared against.

This concept appears to violate the principle of relativity, but at the same time, our cosmological models require a reference frame to compare against. This is one example of an unsolved problem in GR.

While there isn't a visible dipole in our CMB observations, a dipole would have significant ramifications on our frame-of-refernce models.

Refining the Map and Using it

WMAP and the Planck mission refined our data to a point where we can use it for more interesting measurements.

Image Credit: ESA

The size of each small blob actually corresponds to the curvature inherent in the universe. As when we look far back into space, different curvatures will create different apparent sizes.

Not just that, but we can use the CMB to observe the reverberations of sound waves, this analysis allows us to measure the amount of matter that existed in the early universe.

With both measurements of curvature and matter density, we can estimate both the strength of dark energy and the expansion rate of the universe, allowing us another method to quantify dark matter.

These two data points turn out to be observed using the same phenomena, Baryon Acoustic Oscillations (BAOs) - a future topic (maybe in 2 weeks' time).

Conclusion

The CMB is still being investigated and still being observed. The main reason is because it is our only existing window into viewing the early universe.

Not just that, but the CMB provides important data that gave rise to both inflation theory and the eventual formation of our structure in the universe.

I will eventually cover inflation theory. But sooner, I will talk about BAOs. As they are also a rather interesting discussion in cosmology. The measurement of BAOs is what has led to our current cosmological crisis, where the CMB's measurements misalign with other data points in measuring the strength of dark energy.

As always, please feel free to comment your thoughts, including criticisms. Follow if you want to see more!

[oliviax727]

Physics Friday #4: WTF is Dark Energy/Dark Matter? (Part 2)

Important Note: 50 people is a lot! (well after I blocked all the bots it was under that). And I never expected it to grow so quickly. But also I've noticed that a lot of people move in and out of following this blog. And I think one reason is because some people just want to see the physics/maths/astronomy instead of that plus random shitposts.

So what I'm going to do, is for all future posts like this, put this in a second blog to separate it from this one. And every time I post to that one I'll re-blog it here so that there's space for those who just like to see science-y stuff.

The second blog is @oliviabutsmart.

Preamble

Education level: High School (Y9/10)

Topic: Cosmology, Particle Physics (Astronomy)

This is the second part of three to the Dark Energy vs. Dark Matter post. In this part, I'm going to cover the possible ideas behind what dark matter is.

From the last part, what you need to know is that:

Dark matter and dark energy are completely different things, they're both dark because we can't see it

When we look at galaxies and orbits, what we expect is that most of the mass is concentrated in the centre (galactic bulge)

What we actually end up seeing is that there's a lot more stuff in the outer reaches of the galaxy, and we can't see any of it

This hidden matter, called 'dark matter' is what we have to use to correct our equations

Introduction: The chad MACHO vs. the virgin WIMP

Now unlike what this tile says, I don't actually think that MACHOs are better, it's just a play on- .... you know what I mean.

So, given what we know, we need to find a source for this hidden matter. The best place to start is to take a look at what we do know about dark matter:

It doesn't interact with the electromagnetic force (or if it does, it's very rare) - this allows it to appear as 'invisible'

It does have mass - as it affects the motion of stuff in galaxies

It needs to be plentiful outside of galaxies

It generally doesn't interact with other forms of matter

So now we have three different candidate groups for dark matter:

Weakly-interacting particles, including WIMPs (weakly interacting massive particles)

Really big objects that happen to not radiate a lot (also known as MACHOs)

Modified theories of gravity on the large scale

We also need to worry about the way in which this matter is produced. Which is where the cold-warm-hot metric is introduced. It has less to do with temperature and more with speed, particularly in the early universe (see free streaming length for more details - I'm oversimplifying).

What's important is what this "free streaming length" does. Larger lengths corresponds to the formation of larger structures first, then smaller internal structures later.

A cold dark matter model corresponds to dark matter with a small speed in the early universe. In the current day, we think that this is the best model - as it allows for the formation of galaxies first, then clusters of galaxies later - something that we have observed.

Hot dark matter is on the higher end of the speed spectrum and is more equivalent to the formation of big super-galactic sponges before the individual galaxies appear.

The Jocks of the Galaxies: MACHOs

A MACHO is also known as a MAssive Compact Halo Object

Massive - it's heavy Compact - "self-contained" in a way, it doesn't interfere with stars and it doesn't radiate much Halo - it exists in the galaxy's "Halo", a region surrounding the galaxy

Small or Primordial Black Holes

The immediate thought, right of the bat, is to think of a black hole. I mean, it's heavy, and it sucks up literally everything. You may object because of hawking radiation but it's very difficult to see that. So what we get is effectively no radiation.

The problem comes with the fact that it's heavy. Where are you going to get all of this stuff into one place? And won't you be able to detect the effects of these objects on star systems?

The early universe was small, really small, and there was a lot of stuff all compacted into this area. Is it not possible that portions of space end up "pinched" and turn into black holes? Well, maybe!

These black holes from the early universe continue on into the modern day to form the dark, unseeable 'mass' on galaxies.

The problems come with hawking radiation (and not because of the aforementioned radiating) ... black holes naturally emit radiation. A topic I may cover in more detail in a future post. But for now, because of this radiation, black holes actually shrink in size over time and eventually disappear.

This puts a lower bound on how small a primordial black hole can be. As any smaller black holes would've popped out of existence by now.

We could also opt for using smaller black holes that formed more recently, but that also comes with the initial issue of how do we make them?

Red Dwarfs, Brown Dwarfs, Black Dwarfs, or Rouge Planets

Often stars don't go out with a bang. In fact, it's more likely that they simply fizzle out. Black dwarfs are what results from this. And because of it they're just dark solid spheres of material.

Some stars are just small and dim. Red dwarfs are incredibly, INCREDIBLY common in our galaxy. It might be possible that we don't see them because they are so dim.

Some stars don't even form, they just don't ignite. These failed stars turn into brown dwarfs. They are unusually large gas giants with a faint glow.

Some planets get knocked out of their system - for any reason. These planets, without light, wander the galaxy alone.

These four objects, are large, dark, and too small to really interact with anything. And it might be the case that these rouge objects are more common than we think! Enough to account for the missing mass.

The issue is just how we are able to find them so far out of the reaches of the galaxy. Hypothetically, we could say that because of the lack of abundant gas in the outer reaches we end up with failed or dim stars.

Dark Stars

This is both the most interesting candidate for dark matter, and also the least documented. Primarily because we're talking about objects made of shit we haven't even seen.

Dark stars come in two varieties, ones made of dark energy, ones made of dark matter.

Dark energy stars are effectively legacy candidates of black holes, that the dark energy in the universe 'pinches' like in our primordial black hole scenario.

Dark matter stars require us having some sort of particle concentrated in a star-like object. It is of course, a strange idea, and it additionally requires the existence of small particles contributing to dark matter.

There's actually a good PBS Space Time video on this. And I recommend you watch it as I do not have the chops to understand this stuff: https://www.youtube.com/watch?v=zUhOL38346Y

The Little Nerds: WIMPs, WISPs, and other particles

The easiest (and most likely) answer is that we're looking for some sort of small particle somewhere in the universe in big concentration.

The core idea is of the WIMP, a very large particle (large being relative i.e. as heavy as maybe an atom), which doesn't interact much.

We want larger particles because, well, then we can have less than them. It's easier to explain that then having particles that are incredibly numerous.

But there's also another type of candidate: WISPs. The S stands for slender. Maybe we don't actually require massive particles, maybe we can have a particle that doesn't interact with stuff. That in order to interact with it you have to be really close to it and so you just don't end up interacting with it.

Neutrinos

Neutrinos are the most obvious candidate. Because we already know they exist. And we know where they are produced.

Every time you undergo nuclear fusion, you actually produce neutrinos as a bi-product. When you have collapsing and exploding stars, this neutrino radiation becomes so numerous it could fry you.

The benefit of neutrinos is that they only interact via the weak force, which only operates when you're really close to the neutrino. This makes neutrinos a type of WISP.

So why do we not declare that this is dark matter? The issue is that neutrinos are hot dark matter. So if they made up dark matter it wouldn't fit with what we see when we look outside.

We could go for a new, yet similar particle, the sterile neutrino. However we end up falling into the same pattern of needing to find an undiscovered particle.

The Axion

Axions are a hypothetical WISP particle that interacts using either the strong force or the electromagnetic force. They are our best traditional candidate for dark matter. A particle that does exactly what we want it to do.

It's sort of like the "string theory" of dark matter candidates, the cleanest looking idea which we still don't have good evidence for.

Strangelets

Strangelets are particles containing the strange quark. They are candidates for dark matter because they fall more into the WIMP class than anything else.

The scary consequence of these particles is that they become more stable with more particles, so they could effectively turn other matter into strange quarks until an entire planet or star is consumed by them.

Fuzzy Dark Matter

Sometimes when you need a big particle, you actually should look for a small one. Fuzzy dark matter basically hypothesises that there are particles that are incredibly light, allowing them to form wavy fields of stuff that contributes to the mass of galaxies.

Quantum Weirdness and SUSY

SUSY, or supersymmetry, is a foundational component of string theory that states that force is directly translatable to mass. That for every fermion particle type, there exists an equivalent particle that acts as a boson. And every boson, there is an equivalent fermion.

You don't need to worry about the difference between bosons and fermions outside of that they are force carrying, and normal particles respectively.

SUSY, and other weird quantum effects are additionally proposed candidates to dark matter, as they can generate new and weird particles or forces that might contribute to the missing mass. But also, they have had a bad reputation in more recent years for returning negative results.

What if Gravity is Just Wrong?

So this is our last category. Forget the large black holes and the tiny new particles, maybe gravity is just wrong! That we got general relativity right on the scales of planets and stars, but not at all when it comes to larger masses like galaxies and clusters.

Modified Newtonian Gravity

Modified newtonian gravity, or MOND, is the idea that, when acceleration is low enough, the motion of particles stop following the rules dictated by newton's laws. Specifically becoming F=ma^2 instead of F=ma.

This, however, implies that ALL of newtonian mechanics becomes affected by this change, so it's often proposed that this modified newton's law affects only gravity compared to other forces like electromagnetism.

We can also develop this idea into our more fundamental understanding of gravity, General Relativity. Using what's known as Tensor-Vector-Scalar gravity.

The problem is that this is a pretty big change to make. Disproving gravity - it sounds less like a sound theory and more like a conspiracy theory. But of course, that's how we would've treated previous theories of gravity when they first came out.

Another problem is that the current proposed MOND theory still requires the existence of some form of dark matter MACHO or particle.

Entropic Gravity

Entropic gravity is another interesting theory, especially because it also acts as a theory of quantum gravity (i.e. solving the biggest problem in all of physics).

Basically, gravity actually doesn't exist, but is instead a cumulative effect of quantum disorder. Emerging in the same way that temperature emerges from the second law of thermodynamics.

This helps us solve the dark matter problem by demonstrating that gravity changes as we scale things up. Similar to how temperature looks different if we were, say, looking at whizzing atoms in a box compared to a warm block of metal. And MOND theories end up emerging if we extend the scales beyond that of stars and planets.

Yet, the problem still remains, that this requires us disprove the existence of gravity. It would take quite a lot to try and do that. Including accounting for how we get from the probabilistic world of the quantum to the tangible normal world.

Conclusion: So ... Which one is right?

Short Answer: None

We don't really have enough experimental evidence to prove any of these to be the true source of dark matter, or even a combination of different sources. There is experimental data of course, we've been looking for ages. But a lot these experiments either don't give conclusive results or just limit the possible ranges of their properties.

The search for dark matter is ongoing, and is still certainly under the works. It's one of the biggest unsolved mysteries in physics, and just like other theories, the ideas we come up with just end up getting disproven or are too hard to prove to begin with.

This post was a whopper! It took a lot more research and reading to wrap my head around all of the different concepts, as it is just beyond my area of knowledge. But hopefully, I at least explained it well enough for y'all to understand.

As always, feedback is much appreciated. I know I didn't cover things in too much detail, but what can you do when there's so many proposals. I more wanted to talk about the general base ideas of each one instead of getting into the nitty-gritty for a few.

Next week I'll focus on something related to computer science, and finally the week after that, cap things off with a discussion on what Dark Matter is!

[oliviax727]

Physics Friday: Electricity and Magnetism - why are they together?

Introduction - WTF is this?

So this is the first post which is pretty different to what I've done before on Tumblr, Reddit, etc. But given the fact that I have a bunch of knowledge on the subjects of physics, astronomy, mathematics, and computer science, I might as well ramble about it somewhere ... and what's a better place then a blog format on Tumblr!

So my idea is basically to do a weekly thing where I wax lyrically about some random topic within the realm of STEM, and let the internet people see it ... or not. I'm more interested in just getting the neat and cool ideas out there. So if you're seeing this and you're interested - neat! If you're not ... well I'm still going to do what I normally do and shitpost.

The topics will also vary in education level from primary all the way to university level. I'll try and highlight that in each post!

Some pre-info

Education level: High School (Y11/12) Topic: Electromagnetism (Physics)

Ok it's Physics time

At some point in your long life, maybe in class, maybe perusing the internet, you might've come across the term 'Electromagnetism' and gotten confused. Not because it's a complex word and it's 3 am but more that it's strange to see such an emphasis on a combination of Electricity (circuits, lightning, etc.) and Magnetism (Bar Magnets, etc.) and well, why is that? Why don't we focus on something like gravity and electricity or some other physical phenomenon? This is a question I often came across in high school. I saw all of the equations that related electricity and magnetism with eachother: Ampere's law, Faraday's law, the motor effect, Electromagnetic waves. But what intrinsically ties these two phenomenon together? After all, we know magnetism comes from electrons, and electricity comes. But still - this doesn't seem to complete the gap.

This was a question that a lot of people were concerned with, until Maxwell, Lorentz, and Einstein came along and changed our understanding of electricity, magnetism, and motion.

To figure this out, we won't actually need special relativity, because we can just imagine scenarios in a low-speed limit. But we still require relativity of a more classical variety.

So how does it work?

Consider a wire with a current running through the wire. Electrons are moving through the wire, causing the flow of current.

Now, because of Ampere's law, we know the wire produces a circular magnetic field around it.

Given what we currently know, the act of having a current - an electricity thing, producing a magnetic field, is really odd. But what if we were to introduce some velocity into the equation?

Say we now place an electric charge next to the wire, and it's stationary. Ignoring gravity for a moment, nothing happens. Why? Well because of the lorentz force F = qE + qvB there's nothing to move it. But now let's move this charged object at some speed along the wire, and let's say it's moving at exactly the same speed as the electrons in the wire. Now we have force! The charge begins to move perpendicular to the field and the charge starts flying towards the wire.

But this is a kinda boring explanation from the perspective of someone standing still, looking at the wire and seeing this happen. What if we were to look at things from the perspective of the charged object?

Well, given the rules of relativity, in the charge's perspective, the electrons are actually stationary, so from here - there IS no magnetic field!

So what happens now? Well because we have a straight line of electrons, and these electrons are still, we now have radially pointing electric field emanating from the wire. Because of this electric field - the charge will begin to move towards the wire, coincidentally at the same rate as what we see the observer.

Now look at what we have here. From the perspective of the stationary wire, a magnetic field is produced. From the perspective of the charge, we have an electric field.

The fact of the matter is that the electric and magnetic fields are the same thing - just from different perspectives. A pure magnetic field is just an electric field viewed from a different velocity, and what you may see as an electric field is just a magnetic field but because we're moving relative to it, it now affects us.

How Special Relativity Comes into this

We can represent this effect using another equation:

E' = γ (E+vB)

Where γ is the lorentz factor. This is where the lorentz invariance - special relativity comes into this. This is a direct solution of Maxwell's Equations.

Let's simplify this by removing the γ in a low-velocity limit, and also multiply both sides by an electric charge term q:

qE' = qE + qvB

E' is the electric field in a frame moving at a particular velocity, whereas E and B are the electric and magnetic fields in a different frame of reference.

Notice how both expressions represent the force applied to a charge. This is a representation of the relativistic interpretation of electric and magnetic fields.

Image Credit: Wikipedia

This image from Wikipedia, it shows the effect I've been talking about but visually. In the top section we have a man standing stationary to an electric charge, which emanates an electric field. From the perspective of the moving woman, the charge produces both a magnetic and electric field.

On the bottom we see the opposite. A stationary man sees a moving charge as having both an electric and magnetic field. But when we move at the same velocity as the charge, the magnetic field disappears and it appears entirely as an electric field.

Conclusion

In conclusion, why electricity and magnetism can be unified is because they are quite literally the same field, but from a different perspective.

Technically speaking, magnetic fields don't exist, they're just electric fields moving at a particular speed. We could also say the exact same about electric fields.

This revelation is what allowed Einstein to simplify Maxwell's equation into just one - using the power of tensors. Because really, the two forces are one in the same!

I very much hope you enjoyed reading this post. I'm going to be doing this every Friday. It's a bit rusty - and you probably had a hard time reading it. Feedback (both positive and negative) is appreciated!

[oliviabutsmart]

Physics Friday #15 [DWQ]: Multiverse theories

Preamble: What is DWQ?

This is another mini-series that will be ongoing. Similar to opinion posts, there is another type of post that I want to explore.

DWQ - Dealing with Quacks (alternatively, Crackpots or Nuts)

Both crackpots and quacks are unified by what they do. They propose there is something "fundamentally wrong with physics" and that they have this new theory that will change everything.

Their theory is about some fundamental truth with the universe. That the "physics establishment" is constantly attempting to chase ridiculous theories because they don't want to accept reality.

A crackpot is someone who generally has expertise in physics, or a related field like chemistry or engineering. Often they are motivated by a desire for fame.

A quack is someone who has no experience in the field, often with a monetary interest in what they are selling.

"Nuts", which is short for "religious nuts" are those who promote their ideas out of faith and a desire to spread their beliefs. They are more likely to strawman existing ideas first.

I hope that you, the reader, can already understand why I don't like these people. They muddy the waters, mess around with science communication, and give the profession a bad rep. They also lie and pedal disinformation, which ends up acting as a gateway to more serious conspiracy theories within the medical or political realm.

It's also important to identify that this acts on a scale. Technically, some string theorists are a lite form of crackpot - particularly in the way they present their theories and ideas to the public.

But they are significantly more respectable than a flat-earther, or a self-help guru, or a evangelical apologist.

The Multitude of Multiverse theories, or the MultiMultiverse

Multiverse theor(ies) are usually strawmans made by religious fanatics. Think PragerU as a great example.

The argument goes like this:

Scientists have no empirical explanation for fine tuning or the reason for the existence of the universe

In order to explain it, they constructed multiverse theory to explain the source of it

By occam's razor, the simpler argument is the existence of a creator entity, that fine-tuned things for us

Of course you can see how bad the arguments are. The problem is of course that science hasn't accepted any multiverse theory.

Multiverse theories are neat explanations or consequences of other theories, but they are either limited in their explanatory power, or their efficacy to test.

But what are the multiple multiverse theories? Here's three that people claim are multiverse theories:

Many worlds interpretation (a QM thing, and only a multiverse theory in pop culture)

Inflation multiverse theory (one possible consequence of the cosmic inflation hypothesis)

Just an actual multiverse theory (arguable cosmic inflation can lie here)

Many Worlds Interpretation

I've already run through the main gambit of what the Everett interpretation is, so I'm going to tackle this from a pop sci perspective.

When you were younger, you might've heard that the many worlds interpretation literally means many worlds. That with every decision you make, you create a new seperate branching reality. And that multiple realities can simultaneously exist.

Of course, there is an issue with this. Mainly that there aren't multiple realities - there is just one reality, in a superposition of states.

This superposition dictates there is one reality, just that this reality is probabilistic. These realties aren't separated by physical space. It's just one big 'wavefunction'.

Decisions in the many worlds interpretations are also examples of when pop sci goes wrong. It's not necessarily the religious nuts who cause this misconception.

What causes more splits in the wave function is the interactions within it. When an electron collides with a positron, when a chemical in your brain goes from one end to the other. Interaction is what creates these splits.

Technically, decisions are caused by the interactions between electrical signals in our brain, and us making a decision often involves interacting with the world around us. This is how the misconception arises, but the reality is that the split occurs well before and well after a choice is made.

Of course, it's important to state that, the many worlds interpretation is still not the "correct" interpretation. What it posits hasn't been proven.

Inflation Multiverse theory

Inflation theory in itself is already a bit on the rocks in terms of an explanation of why our universe is the way it is. There isn't really any way we can use GR/the standard model to explain why inflation happened. At least, without having to add an extra field or constant in our equations.

Generally, inflation is explained using the addition of a new inflaton field, which in the higher temperatures of the early universe, caused a rapid expansion of spacetime.

This rapid expansion is generated by the field living in a heightened energy state.

At some point, the field reaches a sudden drop-off, at which point the expansion rate suddenly slows down to our expected GR level. The inflaton field then remains at a local minima.

Where does the Multiverse theory come into this?

The drop-off of the inflaton field is not universal. It only occurs at particular points in spacetime. This creates a 'bubble' of space that slowly expands in comparison to the surrounding ocean of space that is rapidly expanding.

We exist in one of these bubbles, which expands at a normal rate. But we aren't the only bubble.

There could be several bubbles surrounding us. All separated by physical space that expands at incredible rates. These bubbles create an effective multiverse.

It's not technically a multiverse because every bubble is still in one single physical universe.

Generally, this version of inflation multiverse theory is better accepted as it has inflation theory to back it up. But it's still not provable, so it's not regarded as truth.

The actual Multiverse theories

There are several multiverse theories. But the key thread linking the other multiverses, is that there is no physical way to traverse the space in-between worlds, and that each universe is seperate in beyond a physical capacity.

I can't go into many different multiverse theories, because the main point is that they're all either bullshit or thought experiments.

One example is the "temporal multiverse theory" which states that time is actually a 3-dimensional quantity, were our multiverses are caused by separations in time.

When you go back in time and alter the past, you end up in an alternate timeline future. This is a common way to interpret most time travel movies or scenarios.

Another is the "10-dimension" theory. There are 3 dimensions of space, 3 dimensions of time, and 3 dimensions of "universe". What is this universe dimension? Well it's effectively supposed to be an altering of the fundamental physical parameters.

The problem is that we don't think that the universe happens to perfectly have three degrees of freedom in it's construction.

The 10th dimension is usually unexplained in this theory.

So what was that fundamentalist strawman about?

There is an idea in physics called "quantum darwinism". This theory basically states that from the many worlds interpretation, there will be one probabilistic reality where human consciousness lives in. And thus that version of reality will be the one we see, as it was fit for human life.

This principle can be extended to various different versions of multiverse theory. That out of the many possible realities, we observe the reality that created the perfect conditions for human life.

This argument, that the universe was predisposed to observation, because it had to circularly, is called the anthropic principle. It can be said that it's an extension of the copernican principle.

And that's it. That's the strawman. Of course, this form of darwinism is not really an actual theory, more a thought experiment.

Conclusion

This post is slightly less long than the other ones but still a lot. Oops! Ruh roh!

Anyways, I hope y'all like this post with a different topic. They will be rarer because I want to take my time tackling these types of posts. Please lmk if you think this post was informative or if you'd like to see more!

Next week will probably be on Baryon Acoustic Oscillations. Follow if you wanna see more!

[oliviabutsmart]

Physics Friday #18: Sounds of the CMB - Baryon Acoustic Oscillations

Introduction: What Are BAOs?

It's time for colours!

Let's break down the term Baryon Acoustic Oscillations (BAOs) ...

A Hadron is a particle made of several quarks, a Baryon is a Hadron that contains an odd number of quarks.

Baryonic matter makes up a majority of the stable, visible matter in the universe. Both protons and neutrons are types of Baryons, so most Baryonic matter is, shockingly, atoms.

Acoustic generally has two definitions, one musicological and one scientific. Scientifically, any 'acoustic' thing involves sound. Specifically here, we're using it to discuss the production and propagation of sound.

Oscillations is a term very related to sound, if you read my posts on the mechanics of sound, oscillations, waves, periodic motion, are all the same phenomena.

Here, an acoustic oscillation is just a looping/repeated physical motion in a medium, like plasma.

Thus, putting everything together, a BAO is the physical motion in a plasma of hydrogen/helium, caused by the propagation of sound waves.

How do they form?

After the era of nucleosynthesis, but before the era of recombination, the universe was full of an opaque plasma of hydrogen/helium.

Sound waves require something that can create both a compression and expansion of this plasma, causing a pressure wave. A force that can pull things together and push things apart.

Thankfully, gravity is a great mechanism to pull things together. All that is required is a few thousand years, and some already pre-existing variations in density to get going.

So this plasma, in more dense regions, begin to pull more matter into those regions, creating a self-reinforcing cycle.

But how do we create the effect of expansion?

This plasma, is, well, hot. Very hot. And because it's everywhere, there's a lot of radiation being constantly emitted and re-absorbed.

When you begin to concentrate a lot of plasma into one location (thanks to gravity), you also concentrate the release of radiation.

Moreover, the speed the plasma accrues when it starts falling into the dense regions will also give it more energy, causing even more radiation to be released.

The effect is that in these denser clouds of gas, more radiation is produced. This produces a radiation pressure, which attempts to force atoms out of the dense regions.

Because of the every-where-ness of this plasma, the radiation pressure is strong enough to completely counteract gravity in some cases.

This generates sound waves, created by the constant tug-of-war between radiation pressure and gravity. These sound waves propagate throughout the early universe.

In Comes Dark Matter

Dark matter is predicted to represent a majority of the matter in our universe, because it is dark, it does not experience radiation pressure.

But because it still has mass, it does experience gravity. This means that the dark matter will stay within the denser regions without rebounding at all.

The dark matter within these regions are what allow regular matter to constantly fall in and out. Without it, the radiation pressure would blow apart the region and it'd become devoid of matter.

Freezing Things in Place

Suddenly, the universe cools to a point where, near simultaneously, matter cools to the point that it can exist as a gas rather than plasma.

Unlike plasma, gas does not absorb all forms of electromagnetic radiation. This is because electrons are now bound to their respective atoms.

This means that radiation pressure no longer comes into effect, and any radiation emitted at the moment of this cooling is free to travel across the universe.

The newly freed radiation is what we see in the CMB - but there's something important about it. It records a single snapshot of the current state of the sound waves propagating in the universe.

Imagine you have a high-speed camera and take a photo of a guitar string being plucked. At that very instant you can see the wave frozen in place, and can use that to determine it's properties.

Image Credit: Reddit

The remaining oscillations in the matter freeze too, allowing for the formation of our modern galaxy clusters, galaxies, and even stars.

How we Look at the Sound

Using the image of the CMB, we can measure the ripples of the sound waves using a Fourier analysis of the temperature gradients.

The temperature is used because it correlates to regions of high or low density, of course, the hotter a location is in space, the more matter managed to get in there, thus releasing more stuff.

A Fourier analysis is a very common technique in sound measurements. It takes any arbitrary mathematical function, and converts it into a frequency spectrum.

A Fourier analysis. On the top, the original signal, on the bottom, the signal's frequency spectrum Image Credit: The Mathematics of Waves and Materials Blog

We can conduct a Fourier analysis in two dimensions as well, we just perform two applications of the Fourier transform, but in two directions.

A 2D Fourier analysis. On the left, the original image, on the right, the image's 2D frequency spectrum Image Credit: Python Coding Block

We can then take this 2D image and plot it on a graph of the distance from the centre.

Applying the analysis and the plotting function to an image of the CMB we get this graph here:

Note that 'Multipole moment' is, for the sake of simplicity, a frequency spectrum Image Credit: Report of the Dark Energy Task Force, 2006

The above image is referred to as the power spectrum of the BAOs.

Adding constraints to Dark Matter/Energy

Dark Matter and Matter Density

The BAOs at the moment of them freezing become an incredibly useful measurement for the propagation of Dark Matter and Dark Energy.

Of course, dark matter is built into the equation, as they form a necessary component of the gravity force pulling things in. We can use the relative strength and period of the oscillations to estimate the amount of dark matter and it's ratio to Baryonic Matter.

Curvature

We can also use our graph for a second purpose: measuring the curvature of our universe.

You see, given the fact that our galaxies and galaxy clusters eventually end up forming from those regions of dense gas, and given that we know how 'far away' the CMB is (thanks to redshift).

We should know the approximate size of these dense gas regions in the CMB, given a certain curvature.

This will appear on our power spectrum as the shift in our graph, the location of our peaks along the x-axis.

In a universe that is hyperbolic, we should expect the density blobs to be small, and in a spherical universe, blobs that are larger. What we end up seeing is approximately a flat curvature.

Dark Energy

Now, thirdly, we can estimate the density of dark energy in our universe.

We can get this easily by measuring both matter density and curvature, as the two are related to the dark matter density.

But, we can also estimate it directly from analysing the power spectrum directly.

Dark energy affects the expansion of spacetime via the Friedmann equation, controlling for matter density, we can use the equation to quantify the Hubble parameter.

The size of the Hubble parameter, relative to our current Hubble constant, can be measured from the fact that the BAOs provide a standard measure of distance.

By analysing the power spectrum, we can effectively work backwards to derive a measurement for the Hubble parameter, and thus the presence of dark energy in the early universe.

Conclusion

Surprisingly a shorter-ish post this time, good on me.

Anyways I'll probably take a break for next week, as it's Christmas. Outside of that, I don't really know what else to say.

Follow if you want more, gib feedback on my post, and comment/repost your thoughts!

See ya later!