Observation 1.
If the two polarizers have the same orientation, the two photons always do the same thing: Either they both pass through the polarizers, or both are absorbed by the polarizers.
Observation 2.
If the angle between the two polarizers is 30°, the two photons do the same thing 75% of the time. 25% of the time, one passes through its polarizer, while the other is blocked.
Observation 3.
If one of the polarizers is horizontal and the other is at 60°, the two photons do the same thing 25% of the time.
This is based on real observations; this isn’t made up.
We want to determine whether the photons have their polarization properties all along, or whether the photons are in some kind of mysterious indeterminate state prior to reaching the polarizers.
Let’s assume that the photons have “hidden properties” prior to observation; observation merely lets us view the properties that the photons had all along. Let’s see where this assumption leads.
The hidden properties of a photon might be this:
(Would pass through a horizontal polarizer. Would be blocked by a 30° polarizer. Would pass through a 60° polarizer.)
It took a lot of words to write that. Let me represent exactly the same thing in abbreviated form:
(Horizontal → Pass. 30° → Block. 60° → Pass)
If one photon in a pair has these hidden properties, the other one must have the same properties. To understand this, suppose one photon in a pair has the hidden properties listed above, and the other one has these properties:
(Horizontal → Block. 30° → Block. 60° → Pass)
This says that if both polarizers are horizontal, the two photons do different things, which contradicts Observation 1. So the two photons in a pair must have the same hidden properties.
Let’s consider again the first example of hidden properties:
(Horizontal → Pass. 30° → Block. 60° → Pass)
If all photons had exactly these properties, the photons in a pair would always do the same thing (Pass) whenever one polarizer was horizontal, and the other was 60°. But this should happen only 25% of the time, according to Observation 3. So a certain fraction of photons might have the hidden properties listed above, but other photons must have different hidden properties.
Now, let’s list all possible hidden properties, in four groups. Two sets of hidden properties are in each group. Group 1: The two photons do the same thing, regardless of the orientation of the polarizers.
(Horizontal → Pass. 30° → Pass. 60° → Pass) and (Horizontal → Block. 30° → Block. 60° → Block)
Group 2: The two photons do the same thing, unless exactly one of the polarizers is horizontal.
(Horizontal → Pass. 30° → Block. 60° → Block) and (Horizontal → Block. 30° → Pass. 60° → Pass)
Group 3: The two photons do the same thing, unless exactly one of the polarizers is 30°.
(Horizontal → Pass. 30° → Block. 60° → Pass) and (Horizontal → Block. 30° → Pass. 60° → Block)
Group 4: The two photons do the same thing, unless exactly one of the polarizers is 60°.
(Horizontal → Pass. 30° → Pass. 60° → Block) and (Horizontal → Block. 30° → Block. 60° → Pass)
Our final task is to determine the fraction of photon pairs that have hidden properties from each of the four groups. Let F1 be the fraction (between 0 and 1) of photon pairs with hidden properties from Group 1. F2, F3, and F4 are similarly defined.
Now, let’s consider Observation 3, based on one horizontal polarizer and one 60° polarizer. The two photons do the same thing 25% of the time. Which of the hidden properties make the photons do the same thing for this combination of polarizer angles? Groups 1 and 3. This means that 25% of photons pairs must have properties from these groups:
F 1 + F 3 = 0.25
Next, let’s consider Observation 2, in the specific case of one horizontal polarizer and one 30° polarizer. The two photons do the same thing 75% of the time. Which of the hidden properties make the photons do the same thing for this combination of polarizer angles? Groups 1 and 4. This means that 75% of photons pairs must have properties from these groups:
F 1 + F 4 = 0.75
We repeat for the other case of Observation 2, with one 30° polarizer and one 60° polarizer. The two photons do the same thing 75% of the time. Which of the hidden properties make the photons do the same thing for this combination of polarizer angles? Groups 1 and 2. Therefore:
F 1 + F 2 = 0.75
Finally, we use the fact that the sum of all fractions is one:
F 1 + F 2 + F 3 + F 4 = 1
If you subtract the first three equations from the last one, you find F1 = 0.375. Plugging this into the first equation yields F3 = −0.125. But we can’t have a negative fraction of photons! Therefore our assumption of hidden properties is disproven! The photons do not have their observed properties prior to observation; prior to observation, the photons are in a mysterious indeterminate state.
© The Author 2017
Michael Brotherton (ed.)Science Fiction by ScientistsScience and Fiction10.1007/978-3-319-41102-6_7
Upside the Head
Marissa Lingen1
(1)Minnesota, USA
Marissa Lingen
Email: [email protected]
20 February 2025
A professional hockey team funds research into concussion-induced brain damage, but the principal investigator worries about reaching her patients as people, not players.
I wasn’t there to see it. I don’t supervise the patients’ lounge, mostly. Ben and the rest of the nurses and orderlies do that for me. I observe the patients in careful, clinical settings. I write up careful, clinical notes. All the useful information that isn’t quite so careful and clinical comes to me through Ben and his team.
“Peter has a broken wrist and three broken teeth,” Ben reported to me after it was sorted out. “Could’ve been worse. Nearly was. But Stosh was clearly winning, so the other boys didn’t jump in on his side against the cop.”
“What about Kendra?” She was the odd one out among our patients, the only one not tied to the Michigan Squids hockey franchise: a combat veteran, there so our sponsors looked good for Supporting Our Troops.
He shrugged. “Kendra’s all in favor of law and order, but she knows when Peter’s got himself into his own trouble.”
“And he had.”
Ben eased himself into the chair across from my desk. I could see a bruise coming up under the dark skin of his chin, from where he’d taken an elbow or a head-butt, separating the two of them. “It was about the team. What they had or hadn’t done to Peter’s brother. Who loved Peter’s brother, who supported him. Whether he was or wasn’t a junkie.”
“So…nothing left untouched.”
“Basically.”
“Peter’s lucky the rest of the boys didn’t pile on.”
“Yep. Well. Ed might’ve added a choice comment or two. Ed might even have started the commentary. But I managed to keep him out of the actual brawl.”
I shook my head ruefully. In his mid-sixties, Ed could afford to leave the fighting to the younger men, but that didn’t mean he always had the sense to do it. He had never been able to keep his mouth shut. In his day, no one wore helmets, much less visors, so you could see him in every game — every minute of footage with him playing — jawing away at the other team, the ref, everybody. All the hits he took to the head had not added to his self-preservation.
Concussion research is like that. They are sweet. They are incredibly sweet. And then out of the blue, they will be triggered by nothing, or what looks like nothing, and there will be violence, or crying, or shouting, raised voices, or just…sullen silence.
Kendra is the worst for sullen silence.
Or there will be gaps, when they stare off into space, just nobody home. Stephane is the worst for that. He doesn’t want to be part of our research at all. His wife
made him.
I don’t know what Ben saw on my face, but he said, “Give it time to work, Catherine.” He calls me Catherine when no one else is around. It’s all “Dr. Huang” in front of patients and staff, but we’ve worked together for decades now. “Rome wasn’t burnt in a day.”
“And amygdalas take time to grow, even in rats, much less in people. I know.” I sighed. “I just — had hoped that they would be done beating the crap out of each other by now.”
“‘Patient socialization is one of the hallmarks of the Squids PCS Research Facility,’“ Ben quoted from our brochure. I rolled my eyes.
Getting sponsorship from the Michigan Squids hockey team really turned a corner for us. It let us do all sorts of things we couldn’t otherwise do — mostly it let us do everything faster. And God knew the Squids had provided us with plenty of test subjects over the years.
Stosh Majewski was the youngest, the most cheerful, the one who seemed the most unlikely to be in a medical research ward all the time — unless you saw his crying jags, his violent spells, his memory losses. Or unless you’d seen the video, which every hockey fan and half the rest of the internet had.
It was the video. The video where an opposing player drove his head into the ice from behind. After that video, it was hard to believe Stosh was alive, much less walking around, talking, joking with his doctors. Hockey fans had explained to me that it was Todd Bertuzzi’s hit on Steve Moore with the volume cranked up to eleven. I didn’t know what that meant. I just knew that Stosh was only twenty-four, and he wanted his balance back. He wanted his memory back. He wanted back in the game.
And his old team, the Squids, had faintly dawning hopes that my amygdala regrowth factor would be the miracle drug that could make that happen.
Amygdala regrowth factor. ARF. Stosh had the other patients barking like dogs when Ben and the other nurses came at them with injections. We needed a better name before we went public with it.
First we needed results.
First we needed the patients to grow enough amygdala back that my best nurse wasn’t beaten all to hell from pulling them off each other.
“Put some ice on that bruise,” I said to Ben. “And if Stosh brings up Jesse again, get him out of the room, fast. Or get Peter out of there.”
“I’ll see what I can do.”
Peter’s brother Jesse was the reason he was in there. The Squids were trying to avoid a lawsuit from the grieving Van den Berg family. Peter had only gotten as far as the minor leagues, then retired to be a cop after one too many hard hits. His brother Jesse was a fan favorite, a gentle giant with the fans and the last of the great enforcers on the ice.
He’d died in agony of a drug overdose. None of the fans had known until it was too late. He’d come from a cop family. It seemed so unlikely. But the pain from the fights, the brain damage from all the concussions — his judgment was shredded. And the Squids’ team doctors…let’s say that one of my conditions when they hired me was that I didn’t have to meet with the team doctors. I wasn’t going to shake any of those guys’ hands.
Ben shook his head. “Give it time, Catherine,” he repeated. “It’s a long game.”
He left my office. I looked at the rest of the files. I couldn’t see anything yet. Maybe there wouldn’t be anything to see.
They all had hope. I would have to.
24 February 2025
Stephane’s wife came to visit today while I was having a session with him. Claire. Her English is so great. She’s never complained about having to move to Michigan for the treatments, even though I know it was hard for her to find work, even though she knows no one but the other Squids’ wives.
“You’re making progress, I can tell,” she said.
Stephane looked away dismissively. That’s all he ever does. I felt like I had to look away, too; I left the room to give them privacy. I know that one of Stephane’s main symptoms is depression, but in this case he’s right: his memory loss isn’t showing any improvement so far. Maybe that means he’s one of the placebo patients. Maybe the ARF just doesn’t work on humans, or maybe it can’t undo the damage from old trauma as much as we’d hope — just stop things from getting worse.
I went down the hall to look in on the patient lounge. They had a hockey game on. I’ve tried to learn the game better since I started working in a Squids-funded facility, but to tell the truth I can never recognize offsides, never.
I almost walked past, and then I heard Ed and Stosh reminiscing. They sounded like old drinking buddies — not arguing, just shooting the breeze.
“I haven’t seen a hat trick that pretty since Bruno Detwiler in ‘22,” said Ed.
“March of ‘22, yeah,” said Stosh. “That was my second year. God, that was a great hat trick. No assist on the third goal, either, and not an empty netter.”
I froze. Only three years ago. One of the hallmarks of their kinds of brain injury is difficulty in forming and accessing memories from recent years. Was I reading too much into this? I went and wrote it in my notes anyway, just in case.
“Put a sock in it, boys, we’re trying to watch the game,” said Peter good-naturedly, and no one jumped on him.
20 March 2025
I got a call from the Squids organization today, what they insist on calling “the front desk.” (To me the front desk is my secretary, Wescott.) “Great news!” said the suit, whose name is Bill. “Looks like we’re for sure going to make the playoffs this year. Got a pretty good chance at the whole thing!”
“That’s great!” I said. I think I even managed to sound sincere, too. It helped that Ed had performed better on one of the memory tests than he ever had, so I was in a genuinely good mood. Ready to be happy about other people’s triumphs.
“We’re going to want a news spot about your research for the period breaks,” he said, like it was the most natural thing in the world.
“I…beg your pardon?”
“A feature. Just a puff piece, one of those misty feel-good journalism thingies,” he said. “Our press gal will set it up with you.”
“My patients are in a very delicate state, Bill,” I said. “It’s the early stages of their amygdala regrowth. I really don’t want them disturbed.”
“I understand,” he said. “It’ll all be very gentle, very soft focus. No hard-hitting questions. It’s not like you’re going in front of the Inquisition, ha ha ha.”
“Ha ha ha,” I said dutifully.
“But we’re not in this for our health, you know. We want to get some good PR out of it.”
I knew what I was doing when I left Michigan State. Or I told myself I did. “PR. Of course.”
“Great! I’ll have her set it up with you. I’m sure it’ll tug everybody’s heart-strings, you’ll be fabulous. You always look so serious and scientific.”
I wasted probably five minutes after terminating the call trying to figure out whether that was a racial remark. I decided I didn’t care. I called Ben into my office.
“Brace yourself, the TV cameras are coming in.”
What Ben said should probably not be recorded for posterity, but we’ve known each other long enough that he knew I felt the same.
He did, however, tell me that when one of the orderlies ran Kendra’s foot over with a cart, Kendra not only didn’t punch her, she said, softly, “Hey, hon, it’s okay. We all make mistakes.”
And then went to talk to Ed about Ed’s kids and their vacation to Florida, what she had liked best about her own Florida vacation before she was deployed.
Is that…apathy lifting? Empathy, control of temper, management of memory? All at once?
Or is it just a good day?
Good days don’t count until they add up. Write it down. Write it all down.
22 March 2025
Claire has heard about the TV spot. She came into my office worried. “They’re not going to mention Stephane’s drinking, are they?”
“I don’t think so,” I said.
“There was — ” She he
sitated. “The DWI. It was a matter of public record. I don’t think we can hide it, Dr. Huang.”
“This is not investigative journalism, Claire.” I knew I was supposed to do something to make a connection, so I reached across my desk and patted her hand awkwardly. “The team is doing this. They want everybody to feel good about the players, about the research they’re funding. That means showing health, recovery. Not darkness and mistakes.”
She looked unsure.
“They’ll probably mention — in general — that one of the symptoms that some people have is difficulty handling drugs and alcohol. And they may focus on Jesse, with that. But I’ll speak to the producer, make sure they know of your concerns.”
Claire’s hand flew to her mouth. “Jesse. I hadn’t even thought of Peter and the rest of the family.”
“I will — ” I wanted to tell her I would handle it. I still want to say I can handle it. But they have the final word on funding. They’re going to do what they’ll do. “I will let them know.”
Speaking of the final word, the front desk — not Wescott, the other one — has let me know that ARF has been renamed cephalladine in time for the video shoot. This is supposed to sound vaguely reminiscent of squid, for the Squids fans who are smart enough to know root words, and just generally scientific for the rest.
I have told the patients. They are still barking at it. Ed tried making wiggly squid fingers, but no one else picked that up. Ben told them if they barked on camera, it would get cut out of the footage and also he would tell the kitchen that they didn’t like peanut butter pie for desserts any more.
Much grumbling. Less barking.
29 March 2025
It could have been much more catastrophic, this video shoot. There were some volume control issues. Even with the ARF — excuse me, cephalladine — some of them just don’t have any idea of how loud they’re talking. Even when they’re not agitated. Maybe that’ll get turned down in production. Maybe it’s just the sort of thing they want.
Science Fiction by Scientists: An Anthology of Short Stories (Science and Fiction) Page 12