The Price of Pride (14/?)
[ canon • Aemond x Royce • female ]
[ warnings: kind of fingering, targcest stuff, smut, the angst, sexual tension, imprisonment, abuse of power ]
[ description: Prince Aemond finds a solution to the disproportion in the number of dragons between Dragonstone and King's Landing: he decides to find dragon blood and, like his half-sister, train dragon riders. He takes as his target the daughter of Daemon Targaryen and Rhea Royce, whom he abducts and imprisons in the Red Keep. Slow burn, darkish, insolent, arrogant Aemond. I have combined several requests here: (dragon blood female & prisoner female). ]
* English is not my first language. Please, do not repost. Enjoy! *
Next chapters: Masterlist
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"Tell him the truth. Lying to my grandfather serves no purpose anyway. He's a skilled player. You have to win his trust." Said her betrothed, walking around her chamber with his hands folded behind his back as if it was simple, while she sat on her bed, looking at him in horror.
Lord Hightower had many reasons to doubt her loyalty, starting with her treacherous bloodline to the fact that, in all probability, Gwayne had convinced him that she had forced her way into his grandson's heart through his bed like a simple whore.
She lowered her gaze, fiddling with her fingers in nervous reflex – her lēkia approached her and knelt before her on one knee, taking her hands in his, slightly rough from holding the hilt of his sword.
"My grandfather is loyal to our family. I trust him. Do it, zaldrītsos."
Otto waited for her in the royal gardens in complete solitude, under one of the beautiful ancient arbours overlooking the sea. The day was sunny and hot, so she was dressed in one of the gowns of fine, thin fabric that she had ordered with her Prince's permission – she could have worn a garment belonging to his daughter, Queen Alicent, but she feared he would perceive it as an attempt of manipulation.
She was to be honest with him, as her betrothed demanded.
She sighed quietly, seeing his seated silhouette in the distance, silver trays full of lemon and apple cakes, caramelised dates, grapes and strawberries on a small white table in front of him. She blinked, coming closer with a rattle of stones under her feet, standing in front of him, feeling her heart stop in her throat.
Otto gave her a gentle, reassuring smile and held out his hand in front of him, pointing to the empty chair across from him, seeing how tense she was.
"My Lady. Thank you for agreeing to speak to the grumbling old man and listen to his concerns." He said lightly and she swallowed hard, sitting down, placing her hands on her thighs.
"Treat yourself. My daughter loves caramelised dates." He said and reached for one himself, taking a bite of it.
He chewed it and swallowed, nodding appreciatively, as if indeed their flavour appealed to him too.
"Do you know what my grandson's – and your betrothed's – favourite dish is?" He asked, looking at her curiously, as if he was challenging her.
She raised her eyebrows and shrugged her shoulders, involuntarily grinning with amusement.
"I don't think such considerations occupy his head. He rarely delights in food, and if he does, it is more in the privacy of his own mind." She said calmly.
Otto hummed under his breath, as if her answer satisfied him, and nodded.
"Our Prince is a man of principle and loves simplicity. Deliberations on trivial things bore him and arouse his frustration, just like the romantic courting of women." He said, spreading out comfortably in his chair, placing his hands on the armrests, asking her the obvious question between his words.
How had she managed to seduce him?
She huffed under her breath and turned her gaze away, looking out at the sea stretching around them, the pleasant fresh breeze and shade cooling her sun-warmed skin.
"Like any man, he is not fond of empty words. He chooses his own deliberately and expects others to do the same. Unless he becomes enraged – then his fury erupts like a volcano." She said lightly, for some reason feeling no fear at the thought.
She had ceased to fear him long ago.
She knew that even if he wanted to, he wouldn't be able to truly hurt her.
"The letter you found in your chamber was sent to you on my command." He said calmly.
She froze, staring blankly ahead, feeling her heart begin to pound like mad.
It was a trial, she suddenly realised.
He wanted to see if she was trustworthy.
For some reason, a wave of sadness and disappointment rippled through her heart.
She naively believed for a moment that her person could occupy her father's mind.
Otto continued, hearing her silence full of disbelief.
"I need to know what you want, child. I need you to put your desires into words so that I can understand what kind of person is sitting right in front of me to become my grandson's wife." He said slowly, as if carefully choosing every thought that left his lips – his voice was gentle and soothing, as if he was trying to reassure her that what she was going to say would remain their secret.
She lowered her gaze, feeling her heart pound like mad in terror – not because she was afraid of him, but because his question startled her.
She didn't know what to answer.
She had never thought about it.
Until now, she had only been the fulfilment of his desires, she thought with shame, playing with her fingers, feeling certain Otto would take her silence as a bad sign, proof that her intentions were not pure.
"I am what he wants me to be." She finally muttered, feeling tears of embarrassment under her eyelids burning as much as if they were living fire.
Lord Hightower looked at her in silence and twisted in his seat with a creak of wood, as if surprised by her answer.
"Do you wish to marry him?" He asked, and she nodded without thinking.
"I want to be by his side. His presence fills my soul and heart with a strange peace. When he is beside me, I am no longer afraid. Of my father, of war, or of what will happen to me. I am not afraid of death or dragon fire. Sometimes I think it would be better for me to die in battle than to live to see the moment when I realise I have lost his affection." She choked out in a trembling voice, feeling the heavy tears one by one run down her cheeks – she was wiping them off the warm skin of her face with her hands, but they flowed anyway.
Why had she said that?
Why was she letting him know her weakness?
Maybe because deep down she hoped that he would kill her one day, she thought.
That he would not let her live to see the day when her husband would love another woman.
"Our Prince holds you in a respect and esteem that he has never bestowed on any woman before. He allows himself to be vulnerable and weak in your presence. Men, dear child, experiencing physical fulfilment without a soul bond, feel an emptiness after the act. Their desire is like a cry of desperation for purely childlike attention and tenderness – then, in his chamber, seeing him in your embrace, I saw a boy who feels protected and comforted. I'm afraid that my grandson fell in love with you."
She swallowed with difficulty, choking on her own tears, looking at him in disbelief, her heart pounding in her chest like mad.
I'm afraid that my grandson fell in love with you.
She shook her head, feeling that she could not accept those words.
He desired her, he enjoyed her, he was fond of her, but he did not love her.
"I dearly loved my late wife. She was my closest confidante, my beloved friend, the most beautiful of women. She was strong, and my grandson is weak. Filled with complexes, he lives to prove his worth, power and strength, not seeing that he is crushing the efforts of many years, made by me and his father. He needs guides, trusted advisors who love him and who want him to prevail. I know that it was because of you that my grandson told his brother about his plans regarding Rook Rest's. I know that you advised him against plotting behind Aegon's back and sought to rally them. You advise our Prince wisely and I wish you to be his wife. As the daughter of the Lady of Runestone, you are the blood of the Kingdom of the Mountain and the Vale, which will be crucial to us when the siege of Harrenhal begins. Your task to the Kingdom will be to rally the Lords against Lady Arryn's will and to stop my grandson from acting recklessly and violently. Do you understand what I have in mind?" He asked calmly, and she nodded quickly, wiping her hot, swollen cheeks with her hands.
"Yes."
As she was fitting her wedding gown, letting the servants and seamstresses check the length of the sleeves, she thought about Otto Hightower's words and how much they surprised her.
He was a shrewd and enlightened man, of that she was convinced – he also let her know that he did not see her as an enemy or a threat, but as an opportunity for them and the Kingdom as a whole.
For some reason, something in his words and the way he said them comforted her – she felt that, at last, the burden of the war and the Crown would partly fall off the Prince's back, allowing someone more experienced to advise him on difficult and complicated matters that would have overwhelmed the wisest of men.
She shuddered as the door to her chamber opened and her betrothed stepped inside, searching for her with his eye.
"No!" She squealed, fleeing behind the light-coloured three-door screen standing nearby. "It brings misfortune. Leave."
He shouldn't see her in her wedding gown before their nuptials.
She heard his sigh of impatience and his lazy footsteps on the other side – when he stopped the servants bowed to him and left the chamber, leaving them alone.
"What did he say?" He asked calmly.
She sighed quietly, stepping closer to the wall of thin material behind which she could see the shadow of his tall figure.
"That he wishes me to win the support of the Lords of the Vale for you. That I would help him control your impulsive nature." She said, and he snorted, frustrated, turning his head to the side.
"Is that how he sees me? As an uncontrollable animal to be tamed?" He asked with a regret that made her swallow hard, her fingers touching the fabric as if she wanted to touch his chest.
His heart.
"No. But he and I know what your anger means and how dangerous it can be. That it is only when its first wave passes that your coolness and common sense returns to you. There is a fire running through your veins – that is your nature. We do not want you to burn in the heat of your own fury, regretting later the deeds done in a sudden burst of rage." She muttered and heard him draw in a breath, as if her words pained him.
"He is disappointed in me, then." He said coldly and she closed her eyes, feeling helpless against his low self-esteem.
"No, brother. He wants your victory, exactly as I do. If you craved sweet lies, you would allow Larys Strong to pour poison into your ears, surrounding yourself with lords who would praise you and your greatness. You, in your wisdom, sent for your grandfather, who is sincere, who cares for you and your family."
"Ours." He corrected her, and she smiled involuntarily with gratitude.
"Ours."
She heard him take a step towards the screen, his forehead pressed against the material – she did the same, on the other side, hearing his quiet breath.
"– I desire you –" He whispered, and she sighed, feeling his words in her nipples, her lips, the tips of her fingers and her throbbing, swollen cunt.
"– let's last until our wedding – let's make this the night we've waited and longed for –" She said in a breaking voice, feeling that she was losing the battle with herself, his scent, his presence, his closeness making her grow hot.
"– what are you suggesting? – that you won't spend upcoming nights in my bed? –" He exhaled, placing his hands on the screen wall, and she felt a wonderful shiver of pleasure run down her cheeks, along her breasts and down her spine.
"– lēkia –" She gasped and they both sighed as the door to her chamber opened and Lysa stepped inside, holding in her hand the jewellery casket she had ordered for the occasion.
"– leave us, brother –" She whispered in a trembling voice, feeling her womanhood pulsing greedily around nothing, a drop of her wetness running down the inside of her thigh.
"– visit me tonight –"
"– I can't – for at least a few days let me pretend I have dignity –" She mumbled and heard him swallow hard, as if her words caused him pain.
She knew he hesitated, that he wanted to say something more, but resigned – she saw him turn and move towards the door, Lysa bowed to him as he left the room without a word.
She exhaled loudly, stepping out from behind the screen, and Lysa gave her one warm, comforting smile.
She was her only friend.
"They have arrived, my Lady – hair adornments, a dagger and a necklace, matching your instructions in every detail." She said, tilting the lid open.
She smiled broadly as she came closer, seeing the objects lying on the cushion – a thin, delicate golden chain with sapphires framed so that they looked like three water drops – two small and one large that was lying between them – her hair pins in the shape of forget-me-nots, also made of sapphire stones, and a long, beautiful dagger, her gift for her future husband.
She had chosen her jewellery deliberately – her wedding gown was sewn from fabrics in light blue tones and browns – she wanted to show her future husband her devotion to him and her own allegiance to Runestone at the same time.
According to what she had heard, King Aegon began to slowly awaken, but he was dazed and was merely babbling, fed with the milk of the poppy by the Maester – they wanted to spare him the pain, which must have been immense anyway, looking at how much of his skin had been burned in the fire.
However, the fact that he was regaining consciousness worried her Prince, who pushed for the nuptials to take place as soon as possible – he was afraid that his brother, as soon as he found out about it, would forbid the Septon to marry them out of sheer spite.
They renounced grand ceremonies and processions – their subjects were starving, and they did not want them to think that during their great suffering they were drinking wine and dancing, mocking them.
"Thanks to my spies, we were able to prevent great misfortune – a dozen inconspicuous boats arrived under cover of darkness from Dragonstone to King's Landing, filled to the brim with food. They were to be passed on as gifts from Queen Rhaenyra to her subjects. Instead, the food will be distributed on the streets of the city just before your nuptials, so that the whole Kingdom can rejoice with you." Said Otto during the Small Council meeting – her future husband had dismissed his mother in revenge for her affair with Criston Cole, thus freeing up a seat at the table.
As she was a dragon rider and would be participating in the war, she needed to know what was happening, so she was specifically assigned a seat in the Small Council, right next to the Prince Regent's grandfather.
She threw her cousin a quick glance and saw that he was looking at her as well, his grin indicating that he was more than pleased.
"Excellent." He said.
Her betrothed, in keeping with her wishes, had allowed them to spend the nights before their nuptials apart, she knew, however, that he was frustrated and made that known whenever he could.
"No. You stay, hāedar." He said when he closed the meeting and she stood up as did everyone else gathered.
She swallowed hard when she heard the door close – she saw out of the corner of her eye that he stood from his seat and approached her with a lazy, unhurried step.
She gasped as she felt his large hand on her waist, wandering up and down, his other hand without any warning slipped under the fabric of her gown from above and squeezed softly her silky, plump breast.
She pressed her lips together, suppressing a quiet moan of pleasure when she felt his parted, moist lips run over her neck, leaving a wet, sticky trail on her skin, his hot breath making her cunt, swollen with desire and longing, clench greedily around nothing.
"– stop –" She muttered, grabbing his wrist as his hand from her waist and hip slid down between her thighs, closing on her womanhood.
"– are you touching yourself? – hm? –" He asked coldly and she shook her head, panting heavily as she felt his hard manhood pushing against her buttocks, a drop of cold sweat dripped down her back.
"– no – I suffer just as you do, lēkia – please –" She mumbled and cried out, tilting her head back as his fingertips began to gently tease what was under the material of her dress, a wonderful wave of heat surging through her loins.
"– mmm –" He hummed and let her go, leaving her alone, thirsty and quivering with desire, walking out of the room without even giving her a single glance.
Contrary to what her cousin thought, it wasn't just for him that the wait for their night together was agony – her betrothed demanded that since he couldn't touch her, she couldn't either.
She knew that he also did not satisfy his urges in any way, which made him more mischievous – he would lurk for an opportunity for them to be alone and put his hand between her thighs to caress and tease her, whispering in her ear.
"– beg, and maybe I'll fuck you –" He hissed, her hand clenched on his arm.
"– n-no – please, please, stop –"
He let her go then, his jaw clenched in annoyance and some kind of awe, as if he didn't think she could really stand it – her whole body screamed before his eyes that she wanted it, and yet she still refused him.
It was a sign of strong will for him, proof that her words were not empty and her decisions were final.
On the day the nuptials were to take place, the entire Red Keep was put on its feet – Otto feared an attack from all sides, including poisoning, so guards personally chosen by him went to the Sept, as well as to the kitchens, to keep an eye on the cooks and make sure they didn't add anything to the food.
She was surprised by this, but she felt relieved that her future husband's grandfather was watching over everything.
From the morning, Lysa and the other servants had been helping her put on her gown – it fitted her body perfectly, revealing her cleavage and shoulders – the sleeves of the bottom dress clung to her arms, while the sleeves of her top dress, the blue one, was slit at the elbows, falling all the way to the ground.
Some of her hair was pinned up in a bun at the back of her head, decorated with small sapphire flowers, while some fell in waves down her back.
A necklace completed the look – it adorned her long neck and accentuated the colour of the fabric of her gown, however, she actually hoped that this and her sapphire hair adornments would be the only things left on her body during their wedding night.
She shuddered as the door to her chamber opened and she saw Queen Alicent before her – she stepped down from the small dais and bowed to her as did her servants, whether she wanted to or not having to show her respect.
The Dowager Queen stopped before her and sighed, folding her hands in front of her.
"Do you know what kind of man you will marry? Who my son is?" She asked, and she swallowed hard, wondering how a mother could know so little about her own child.
She thought she was simply afraid of the answers to the questions she was asking herself and didn't want to know them, separating herself from who her son was in her mind.
"Yes, Your Grace." She said calmly, looking her straight in the eye. "Our Prince holds you in deep esteem and hopes to earn your praise."
She saw Alicent's lips twitch, her eyebrows arching in an expression of regret, as if her words had caused her pain, her large brown eyes filled with nothing but sadness.
She nodded, as if accepting her words in her heart, and gestured to her servant, who held a small chest in her hand.
"I wish to offer a blessing to you and my son. I ask that you accept this small gift from me, along with my desire for you to be protected by the gods themselves." Said the Queen and opened the lid – she saw a fine gold chain with a small pendant in the shape of a seven-pointed star.
She nodded, looking at it, wondering if, when she went to see her son, she would find at least a few warm words for him.
The journey in the carriage through King's Landing seemed to last for ages to her – the streets were full of happy people – Lord Hightower, according to his plan, began handing out food to the people, leading to a sudden outburst of joy.
The smallfolk, in keeping with his desire, saw this event as a sign, recognising that the gods had supported the marriage between the Prince and his relative by sending them revelry, putting an end to their hunger.
However, for how long will the supplies stolen from Princess Rhaenyra last?
When will their suffering begin anew?
She swallowed hard at the thought that the war had to end as soon as possible, but both her future husband and Dragonstone knew that neither of them had enough advantage to bring the other to its knees.
When she arrived before the Great Sept and the carriage doors opened in front of her, she froze, feeling panic – the people around her were shouting her name, throwing flowers, reaching out to her as if she were some kind of semi-divine being, a symbol of the life they would never know.
She felt overwhelmed and stunned, alone among the crowd, small without her dragon and bow, dressed in a long gown like a doll.
For some reason she wanted to cry.
"My Lady." She heard a voice in front of her, then saw Otto Hightower walking towards her between the guards. "My Lady, give me your hand."
She swallowed hard and did as he asked, placing her palm on his, rough and large. With his help, she walked down a few steps to a small wooden platform, and from it to the ground, feeling that her legs were trembling with fear.
"I am not your father, but I will be more than happy if you do me this honour. It is a difficult journey and no young woman should have to walk it alone." He said calmly, and she looked at him with big eyes, noticing something in his gaze that could have been sympathy or simple concern.
She had always dreamed of someone looking at her like that.
The way a father would look at his daughter.
She nodded, thinking in the back of her mind that if she let go of his hand she would just fall, her legs soft as cotton wool.
As she walked with Lord Hightower into the Great Sept, she heard the sound of trumpets, young girls, daughters of lords and knights throwing flowers at her feet.
It all seemed unreal to her – the temple around her was so gigantic that it took her breath away, the great, tall statues of the Seven Gods towering over those gathered to form a circle, enclosing the entire structure.
At the very centre, on a raised platform stood the altar at which stood the Grand Septon and her betrothed, a sweet emotion squeezed her throat as she looked at his face.
Though he stood erect, with his hands folded behind his back like a statue, she could see that his gaze was hot, vulnerable, his eye large, his lips parted in a heavy breath as if he longed to cry at the sight of her – the fact that she had chosen not the colour of his or her lineage, but his colour, the blue of his sapphire, something only he could understand, the expression of her devotion, her understanding, her affection.
When they stopped at the steps Otto let her go, but she, seeing her cousin's face felt more confident – she grabbed the front of her gown and lifted it, not wanting to step on it, climbing slowly upwards, her steps echoing loudly around her.
She sighed quietly as she stood in front of them, not daring to look at his face, feeling that if she did she would cry for some reason.
It was really happening.
She was to become a wife.
She looked at him and it was a mistake – she felt a squeeze in her throat when she saw him draw in the air loudly when his gaze met hers, as if he felt something deep inside himself that frightened him, his lips slightly parted in a shuddering breath.
"You may now cloak the bride and bring her under your protection."
Her cousin swallowed loudly, looked at the Septon and then behind him, nodding – Gwayne Hightower approached him with a long black cloak embroidered with green threads from which the figure of a three-headed dragon was formed at the very centre.
The crest of their family and the colours of the Hightowers.
She bowed humbly as he threw the cloak over her shoulders with a sweeping gesture, making sure the material did not slip, and she closed her eyes.
He took her under his protection.
"We stand here in the sight of gods and men to witness the union of man and wife: one flesh, one heart, one soul, now and forever. Cursed be he who would seek to tear them asunder." Said the Septon – her betrothed extended his hand to her, standing proud and upright, so she placed her palm on his – the priest entwined their joined hands with a wide, bright ribbon.
"In the sight of the Seven, I hereby seal these two souls, binding them as one for eternity. Look upon one another and say the words." He said, and they looked at each other, her heart pounding in her chest once before they both opened their mouths and their lungs left the words spoken surprisingly confidently and calmly.
"Father,
Smith,
Warrior,
Mother,
Maiden,
Crone,
Stranger
I am hers | I am his
and she is mine | and he is mine
from this day, until the end of my days."
They fell silent, and though she thought he would not do it, that it would be beneath his dignity, he took her hot cheek in his hand and leaned down, looking at her as if he held the entire heritage of Old Valyria in his fingers.
"With this kiss, I pledge my love." He whispered, only a quiet sigh escaping her throat as his full, fleshy lips pressed against hers in a deep, warm, moist kiss, so tender and soft that she felt a single, lonely tear run down her cheek.
My love.
When he broke the kiss he didn't move away for a moment, just looking at her, and she smiled in a way that must have made him happy, because he smiled too, shyly and sweetly, like a little boy.
They were husband and wife.
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HUP, EPR, and Bell’s Theorem
Abstract
An educational document discussing the Heisenberg Uncertainty Principle, the EPR (Einstein- Podolsky-Rosen) Paradox, and Bell’s Theorem, written for an audience without a background in physics, but with their head still screwed on right.
1 Introduction
Ah, quantum mechanics. A bizarre theory which unfortunately describes our physical world exceed- ingly well. Einstein didn’t get it. Bohr didn’t get it. I don’t get it. And soon, you won’t get it either. As the saying goes, the more you know about quantum mechanics, the less you understand it.
I will be skipping around in terms of topics covered in undergraduate quantum mechanics courses to prepare you for the actual beast, Entanglement.
Entanglement, the property of quantum systems to remain correlated even when separated, is a concept which has transformed from a worrisome byproduct of a thought experiment [1] into a cornerstone of quantum mechanics itself. What is a quantum mechanics? Google is your friend, my dear reader. My time with you is limited„ and I cannot teach you the alphabet to make you read Shakespeare. I can only explain what you directly need to understand this article. Anything else shall be your homework, and if I am feeling kind at the end, I will provide a list of accessible resources on learning quantum mechanics the RIGHT way.
As we dive into the frankly confusing world of entanglement, it is vital that you remember one thing– A quantum particle is described by a wave function, Ψ. This wave function is a solution to the Schrodinger equation.
This is what they mean when they say something is both a particle and a wave; It’s behavior can be described by a special kind of wave equation, which we all know and love as the Schrodinger Wave Equation. But that’s not important right now. I’ll explain more if I need to. We need to get to HUP.
2 Heisenberg’s Uncertainty Principle
Formulated by Werner Heisenberg in 1927, the Uncertainty Principle is an indomitable tenet in the field of quantum mechanics. Its premise is simple. The more precisely a particle’s momentum is determined, the less precisely is its position. In one dimension, this can be summarized with the following mathematical statement: ∆x∆p ≤ 2
Here, ∆x is the standard deviation or “spread” of the position x, while ∆p is the standard deviation of the momentum p. As the spread of one quantity decreases, the other must increase in order to maintain the inequality. I will not bother proving the Principle in full, but I have Heisenberg’s original proof in the references.
Is that it?
Ummmmm, no. An important thing to remember about HUP is that it is not exclusive to x and p. HUP applies to any two quantum mechanical operators, A, B, which do not commute with each other i.e. [A, B] = AB − BA = 0. But that’s all mathematical nonsense, Min! What does it really mean?
Fine! I’m only doing this because it will be useful when we get to measurements in the EPR paradox and Bell theorems. In order to understand what “not commuting” means in the physical sense, let’s use our favorites, position and momentum, as an example. In quantum mechanics, xˆ andpˆ are referred to as the position and momentum operators respectively. (Why the little hats? Firstly, they’re cute, and secondly, well, you’ll see.) The whole point of calling them operators is that they act on wave functions. And in the crudest sense possible (please don’t try this at home, folks), hitting an operator on a wave function and taking the expectation value, gives a measurement of the quantum mechanical system.
There is about three semesters of quantum mechanical education I’m waving off right now, but bear with me. When we act the momentum operator on the system, in some sense we extract the momentum. Same thing for position. However, the whole deal about x and p is that they do not commute. So, the order in which you conduct the measurements absolutely does matter. First measuring x and then p would give you a different answer than first measuring p and then x. This is because the very act of measuring a quantum state changes it. That’s right! It changes. This makes all the difference when you consider the standard deviation of a bunch of measurements. If my memory of introductory quantum mechanics serves me right, after about three pages of algebra you arrive at the familiar position-momentum uncertainty principle.
The moral of the story is that the non-commutativity of these operators manifests as a sort of granularity in the accuracy of measurements you can make on a physical system. This granularity is retained between any other kinds of non-commuting measurements you can make!
On second thought, do you really need this? Probably not. But, the algebra of uncertainty principles is a pet project to me. Especially the strangest of them all, the energy-time uncertainty principle. Enough on that! Here’s the main takeaway (other than the actual HUP statement) that you need from this section:
Making a measurement on a state changes its wave function. No exceptions. None. The detached observer is not a reality in the quantum mechanical world.
3 Spin
I realized that the following sections will not make any sense if you don’t at least know what spin is. So, let’s make a short pit-stop at Spin City to learn about this nonsensical physical quantity.
We’re all aware of angular momentum– its the rotational analog of linear momentum (which we talked about the previous section). We all agree that it is a property related to the motion of an object, right? WRONG! Sometime in the 1900s (Seriously, 20th Century Physicists should chill out), it was discovered this angular momentum from motion i.e. “orbital” angular momentum, as it was called in the atomic physics context it was first described, does not account for all the angular momentum of a particle. Long story short, the remaining angular momentum, which is intrinsic to a particle, is now called Spin. Every fundamental particle has a particular value of spin, which, in quantum mechanical jargon, is the eigenvalue of the spin operator.
For understanding the following sections, we really only need to care about spin-1/2 particles, which are lovingly called fermions, and are the building blocks of all ordinary matter. The shining feature of spin-1/2 particles is that their spin can either be +1 or −1 , which is often referred to as spin-up (↑) and spin-down (↓) respectively.
Physically, the up or down comes from whether the measured spin is along the axis it is measured, or opposite to it. Yes, spin is a vector, so it does have three independent components in the three spatial directions, but it is convention to consider the z-component of the spin for calculations and experiments. Any references to up and down in the next sections are along the z-direction.
Oh, and one more thing, spin-0 particles have no intrinsic spin. This will be important when we encounter the EPR Paradox.
4 EPR Paradox
After skipping a whole bunch of most-likely important concepts in the study of quantum mechanics we arrive at the EPR paradox.
The EPR paradox is a thought experiment first described in the groundbreaking paper [1] by Einstein, Podolsky, and Rosen in 1935. Einstein was quite vocally a hater, and the EPR paradox was proposed as evidence that the description of reality provided by quantum mechanics is incomplete. Reality doesn’t care, of course, and the EPR Paradox isn’t really a paradox. In fact, it is the foundation of entanglement– a magnificent, very real feature of reality which spans black holes, quantum computers and even my field of research: Entanglement in elementary particle physics.
In fact, I’m so self-centered that the example we will use to illustrate the EPR paradox is from particle physics. Just kidding, my explanation follows Chapter 12 in Griffiths’ Introduction to Quantum Mechanics, and is a simplified version credited to David Bohm
EPRB Paradox
Suppose a pion (funky particle with spin-0) at rest, decays to an electron and positron which fly off into opposite directions. Since the pion has spin-0, conservation of angular momentum dictates that the electron and positron occupy the following spin configuration.
√(1/2) (|↑↓⟩−|↓↑⟩)
BE NOT AFRAID of the mathematical jumpscare. The fancy bracket |·⟩ is what’s called a “ket”, and is used to denote the state of a quantum system. All the expression says is that either the electron is
spin-up (+1) and the positron is spin-down (−1) or vice-versa, because the total spin of the system 22
must add up to 0. (Since the initial state is spin zero, the system must stay spin-zero even after the decay occurs. That’s what angular momentum conservation is all about.) We don’t know which combination we will get, but it must be one of the above. Measuring the spin of one of the particles will automatically tell us what the spin of the other particle is. This means that the spins of the electron and positron are correlated. In modern terms, such a state is called entangled.
Now, let’s pretend that these particles fly off in opposite directions, until say, they are several light years apart. What would happen if we found the electron and measured its spin to be +1 ? We instantly know that the positron’s spin is −1 . This is obvious. Why are we mad about this?
Naturally, we may think that the electron really was spin-up from the moment it was created and it was only that quantum mechanics did not know until we made a measurement. But by the principles of quantum mechanics, neither particle had a definite spin, until we made a measurement, causing the wave function to “collapse” and instanteously produce the spin of the positron which is lights years away!
The EPR bros were NOT having it. Einstein famously called this phenomenon “spooky action at a distance”. They stated that the quantum mechanical standpoint must be wrong! The electron and positron must have had well-defined spins from their creation, even if quantum mechanics does not know it. Quantum mechanics is not a complete description of reality and there must be some hidden variables which describe a physical system that we do not yet know.
The fundamental assumption guiding the EPR argument is that no information can propagate faster than light. This the principle of locality. In order to appease this, we can say that the wave function collapsed at some finite velocity and is not instantaneous. However, this violates conservation– If we measured the positron spin as well before the information of collapse reached it, there is a 50–50 chance that both particles are spin-up, which means the system has total spin-1. Preposterous! You can mess with anything you want in this universe, but you don’t mess with conservation laws. What do we do now?
Okay, let’s calm down. The theorists may say whatever they want, but experiment doesn’t lie. Experiment tells us that in these cases, spin is perfectly correlated. The wave function collapse is instantaneous. That’s crazy. Call your mom and tell her you want to go home. The EPR Bros are frightening you— Quantum Mechanics is NOT local so it is NOT complete.
...Except. It is. Enter, Bell’s Theorem.
5 Bell’s Theorem
Now, what’s the situation? The EPR gang is not happy. I’m not happy. You’re not happy. Is quantum mechanics wrong? No, silly! EPR said it themselves: they think it’s merely incomplete. So, in order to completely describe a quantum mechanical state, you not only need the wave function Ψ, you also need some unknown, hidden variable λ. Lots of hidden variable theories were proposed after the Einstein-Podolsky-Rosen paper, but none of them ever gained traction. It was still a respectable area of study until 1964, when J.S. Bell proved that any local (Remember locality from the last section?) hidden variable theory is incompatible with quantum mechanics.
I’ll spare you the details of Bell’s work, dear reader. One thought experiment in an essay is gruesome enough. (It is also getting quite late and I still didn’t code my calculations. I have spent far too much time on this already.)
Bell’s proof involves the wonderful use of probability, and the barest assumptions that can be made about local hidden variable theories. Basically, in any local hidden variable theory, the probabilities of various outcomes are related by what’s known as a Bell inequality. If EPR’s conjecture is right, and there really are hidden variables we don’t know about, then any physical system must obey its Bell inequality.
Except, there have been various experiments since the 1960s confirming that Bell’s inequality is indeed violated. This came as a rude shock to scientists as it is not fun to learn that reality is very much nonlocal. It was all fun and games when this was all merely a mathematical artifact, but nonlocality felt like a gateway drug to a much grimmer violation.
Causality
Bell inequality violations, no matter how surprising, are merely wonderful correlations between two sets of otherwise random data. Sure, the measurement of the spin of the electron affects the positron, but it does not cause it in any meaningful way. The person measuring the electron spin cannot use this collapse of the wave function to send a message to the person with the positron, since they don’t control the outcome of the experiment. They can decide whether to measure the electron at all, but the other person only has access to the positron’s spin and cannot tell whether the electron has been measured or not.
Phew! This sort of nonlocal influence does not transmit any energy or information, so it is exempt from the speed of light. Meanwhile, causal influences, those which do transmit information or energy, cannot travel faster than light. According to special relativity, if this was possible then, there are reference frames in which information can propagate backwards through time. And that, my dear reader, is what we call a big nono. Since the EPR paradox does not imply that causality is violated, we can lie uncomfortably on our bed of nonlocal but causal theory of quantum mechanics.
So rest easy, quantum mechanics is weird, but safe. Entanglement is not a fairytale, but also not the boogeyman. It’s probably more scared of you than you of it. Just give it some time. More answers will follow.
What Do I Do Now?
So, you want to know more? Or curl up in a ball and never think about this again? Either is fine. I won’t judge. If your answer is the former, here are some resources to guide you through the thickets of quantum mechanics.
PopSci Sources
1. IDTIMWYTIM: Heisenberg Uncertainty Principle
2. Why did Quantum Entanglement Win the Nobel Prize in Physics? 3. Bell’s Theorem: The Quantum Venn Diagram Paradox
Surely, you’ll get more out of these wonderful science Youtubers than you did from me yapping for four pages. There are a bunch more probably, but you’ll have to find them yourself.
Academic Sources
1. An Introduction to Quantum Mechanics, D.J. Griffiths.
Of course, there are other quantum mechanics textbooks that I like much more than this one. But, this is the least daunting, so I’ll leave it here.
Don’t forget to like and subscribe for more silly academic style papers.
References
[1] A. Einstein, B. Podolsky and N. Rosen, “Can quantum mechanical description of physical reality be considered complete”? Phys. Rev. 47, 777–780 (1935) doi:10.1103/PhysRev.47.777
[2] Heisenberg, W. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”. Z. Physik 43, 172–-198 (1927). https://doi.org/10.1007/BF01397280
[3] D.J. Griffiths, D.F. Schroeter, “Introduction to Quantum Mechanics, Third Edition” Cambridge University Press (2018) 978–1–107–18963–8,
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title: i'd fight the sun for you, my love
pairing: barbarian!kirishima x borrower!reader
summary: when kirishima finds you, a tiny human(?), stealing from his things, he finds that you've stolen his heart as well.
notes: ask, secret life of arriety inspired bc that movie is so cute, yandere kinda
kirishima was sunbathing out in an open field. he had just finished a long treck through the caverns of a dragon. he was finally shutting his eyes.. when he heard a scuffling noise behind him.
he turned around to see.. a small human grabbing all his jewels? a needle keeping your hair held up, a fitted red leotard and leggings encapsulated you as you stuffed thing after thing into your small bag.
at the realization you'd been caught, you'd dropped all your splendors and ran to go back to your home, a hole in the ground.
it was too late though, the barbarian was faster and caught you easily.
he looked you over, sitting you in his palm as he examined.
"do you.. understand me?"
you nodded, feeling odd under his gaze. you were taught to fear people like him, to never let a human see you, to run as fast as you could away.
this guy was making all your red flags go off. sharp teeth? jewelry? tall? he had abs?
"what are you? some kind of elf?"
"i'm a borrower! not some elf!"
"huh? okay.. ms borrower.. why were you stealing my stuff? that's really expensive you know."
"it's what we do! and you can always get more random guy."
"that's not the point-- it's the principle."
"whatever! let me go to my home!"
"what's wrong..?"
he let you down, bending down to the grass to let you scurry to your home.
he turned around, getting ready to lay back down when he heard rushed running back. you tapped on his legs, tears in your eyes.
"[name]. and there's a- a spider. can you kill it for me? it's in my house!" you wailed, clinging to his leg.
"oh. i got you [name], im eijiro, just.. hold on."
he put you on his shoulder, looking at the small hole you called home.
he set off a bit of fire into the hole, killing the spider,
but burning all your things along with it.
".. did you just incinerate all my stuff."
he rubbed the back of his neck. "oops?"
you yelled directly into his ear, making him promise to travel with you until he got back all your stuff.. plus interest.
he agreed, and so it began.
he grew infatuated you to a strange degree, you'd catch him staring at you often, always wanting you in his arms.
you'd be safe that way, he assured you.
if anything so much as made you flinch it'd get incinerated.
it progressed as your travels did, the satchel with your stuff getting bigger and bigger.
he'd make note of all the things you'd like to eat, to do, to read, he'd fill your days with stories and happy memories.
he'd make sure you slept comfortably, foraging cotton and leaves so you'd sleep on a plush bed.
he'd never make you go hungry, adding days worth of travels onto his journey just to get you your favorites.
he'd dress you now too, grabbing flowers and snipping pieces of his fabric to decorate you.
like a little doll.
but his possessive nature grew too, it started only with bugs, but it ended with creatures. other humans too, he'd even hurt one of your own kind.
but it was all for you wasn't it? don't make him feel guilty, you're just so helpless, so small.
you couldn't leave, you needed your stuff back right? you needed him.
you realized, even though you weren't in a cage, you'd been caught.
and you could never escape the barbarian, who was now planning on taking you to his home. forever.
tag: @eyeofthetiger501
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