Boltzmann’s Brainchild

His head was hurting. His mouth was dry. His entire body felt uninspired and feeble. He was feeling much the ago when he had left the dinner table. How long ago was that? What time was it?

He’d left his watch upstairs and hadn’t the capacity to find a clock right now. But a quick pass by the hall window confirmed that the Sun was coming up. They were firmly in the AM and he was forced to accept that it was no longer the previous evening.

No appreciation for time! Why was that?

He passed through the dining room. The help were busy clearing all the dishes and empty bottles. The clink clink clink of silverware, chinaware, glassware, and napkin rings. To Voskhod’s ears, it might as well have been shelling. It made him want to duck his head, hug the earth, and pray that a stray shell didn’t land in his foxhole.

“I’m sorry, sir,” said the nearest footman. “Was there something you needed?”

Voskhod pondered that for a second. What did he need? Some aspirin and a loaded gun? A kennel? A soundproof room with better security?

“Where’s Baxter?” he asked.

“In the library, sir. He went there once all the guests left.”

“How long ago was that?”

The footman shrugged. “A few hours, sir. Things ended somewhat abruptly once you retired.”

Voskhod placed three fingers to his forehead and pressed against the flesh, as if that would somehow make the headache go away.

“Was their yelling?”

“Excited chatter is how I would put it, sir.”

He found Baxter in the library, as advertised. He was standing in front of a whiteboard. His hands were covered in ink and a small pile of depleted markers lay at his feet. The rag next to them suggested that he had written and erased what he was working on many times over.

Voskhod stopped in the doorway. His footfalls alerted Baxter to his presence. He stopped what he was doing and spun around. The smile on his face faded when he noticed how disheveled his companion looked.

“Did I wake you?”

“I heard noises. What the hell did you do?”

Baxter shrugged. “The conversation turned a bit existential. I needed room to think and they were stifling me. I may have instructed them to leave. In any case, I think I’m onto something.”

Voskhod grumbled. “Okay, tell me…”

“Consider this… the current estimate places the amount of data in the visible Universe at six times ten to the power of eighty bits. That’s every single elementary particle that makes up baryonic matter, reduced to a series of ones and zeroes. Follow?”

Voskhod hummed an affirmative.

“Now — ” Baxter moved to a blank section of the board and hastily scrawled another set of numbers. “The best estimates we have for human brain capacity indicates that two and a half million gigabytes would be sufficient to render a person’s brain functions and a lifetime’s worth of memories in digital form.”

“Right,” Voskhod nodded.

“So — ” Baxter paused long enough to scrawl a third set of streaks on the board beneath the others. “Expressed in the simplest terms, the Universe has the same amount of information as three times ten to the power of sixty-eight human brains. That’s three trillion quintillion quintillion quintillion lifetimes worth of knowledge of experience.”

Baxter underlined this number and tapped his marker against the board a few times for emphasis. His enthusiasm diminished as he noticed the blank look on Voskhod’s face.

“Do you not see the significance of this?’

Voskhod shook his head. “No. Frankly, I don’t see what use this information has.”

Baxter exploded, equal parts ecstasy and anger.

“Think about it! This is just the Universe that we can see! All the baryons in existence, every elementary particle that constitutes matter and the known laws of physics — they account for only 5% of the mass-energy density of the observable Universe. One-twentieth! When you factor that in, you realize just how freakishly advanced the Universe really is.”

Voskhod looked less lost now. “So you’re saying that these numbers are just the tip of the iceberg?”

“Correct! And that’s not even taking into account that there could be so much more information written on the other side of every event horizon of every black hole that’s ever formed. There could be an infinite number of additional volumes in the infinitely dense depths of those behemoths!”

“Which means if this is a massive simulation, it’s far more sophisticated than we could ever grasp?”

Baxter raised his arms in celebration and laughed. Finally, the apprentice understood the master! He looked as though he might break into dance at any moment. Voskhod interrupted the reverie and reiterated his earlier statement.

“I don’t see what use this information has.”

Baxter went from euphoric to angry in the space of a heartbeat.

“Don’t you see it? Since the beginning of time, people have been preoccupied with the idea of a beneficent, omniscient, omnipotent, and omnipresent entity. They always took it on faith that this entity was always watching over them and always with them. What if they were right? What if they merely lacked the means to articulate what they felt?”

Baxter looked off into the distance somewhere. His voice became hushed and reverential as he announced his conclusion.

“What if… we are occupants in a giant Planetarium? The gods are the programmers themselves and the simulation never ends? It just keeps going deeper and deeper.”

“That’s… crazed… or brilliant,” said Voskhod. “I’m not sure which.”

Baxter gasped happily. It was as if the glee that was building up inside him finally found validation and release.

Voskhod seized on the momentary lapse and approached the board. Taking the marker from Baxter’s hand, he added a few addendums.

“So… in this simulation, what are the physics models?”

Baxter looked suddenly confused. “Physics models?”

“Yes. Are they consistent with the laws of the ‘real Universe,’ assuming such a thing exists. Or are they modified for the sake of keeping us contained? And if so, how do we prove it? How do we test this hypothesis?”

For the first time that evening, Voskhod saw the exhaustion in his friends eyes. In addition to the hours he’d spent doing the math, he had spent what energy he had left expounding on it. He took a moment to rally, but the fire in his eyes was gone.

“Okay… as per the original proposal papers, the quantum-physical and thermodynamic considerations would have to be the same for us to obtain accurate estimates of the energy involved.”

Voskhod began making his additions to the board. He started with the all-important equations. The Boltzman Constant and its estimated values for the known Universe:

k = 1.380649 × 10−23 m2 kg s-2 K-1

This was followed by the requisite quantum-statistical models: Bose–Einstein, Fermi–Dirac, Maxwell–Boltzmann. Then came the cosmological principle with which the Universe would not make sense — λCDM. And of course, the most recent estimates for the Hubble Constant: 69.8 km/sec/Mpc.

“The obtained values would need to be multiplied ad infinitum,” Baxter uttered. “Which means the architects must be more advanced than a Type III civilization, possibly Type V.”

“Ah, but let’s not discount Loeb’s Cosmological Conjecture,” Voskhod added, moving to an unmarked section of the board and adding this parameter. “New Universes are conceived by class A civilizations in a cyclic process ad infinitum.”

Voskhod drew back to appraise everything they’d written. He glanced at Baxter, who looked similarly animated. Voskhod lamented that he was about to shatter that so completely. He raised the marker and sliced through the equations he wrote. Baxter was about to object, but Voskhod preempted him.

“Now let’s assume that the laws of physics are NOT the same in every Universe. Either the architects are working with different models each time, or they deliberately chose to alter the considerations for the sake of maintaining control.”

Baxter palmed his face. “Not this again!”

“It’s a logical extension, of both the Planetarium and Zoo Hypotheses! Why keep the physics the same if control is your objective? And need I remind you how naive it is to assume uniformity?”

Baxter grunted. He knew there was no logic in arguing the point. A committed generalist was never going to convince a committed pluralist. Voskhod issued his final argument, spitting out chicken scratches as fast as he could. Each stroke was thinner now, representing the last of the marker’s ink.

“So… if we assume the laws of physics, as we know them, were crafted by a Type A civilization in a previous Universe, then we can assume that the physics model employed was crafted by a different party.”

Voskhod hastily drew two swirling formations , representing Universe A, B. Beneath those, he drew two more to represent their descendants - A1 and B1. They were little more than blots now, as the marker was almost dry.

“Two possibilities present themselves: either the makers used identical models, or they didn’t. If the former is true, then every Universe is guided by physics consistent with the previous Universe, but NOT with each other.”

He placed checkmarks in both the A and B column, then two x’s between them.

“If the latter is true, then that means that every Type A Civilization has designed new Universes with new models. Ergo, no two Universe’s are the same. But if we assume that different civilizations will choose between these two options, then we are left with the conclusion that some Universes resemble their predecessors, while others do not. The endless variation this creates means that there may be a mean model, or not. We’d have no way of knowing without comparing all the Universes that have ever been.”

Baxter’s face dropped. It was as if Voskhod hit him in the face with a hammer. He took a deep breath and looked upon his equations like they were the scene of an accident.

“We can’t,” he said, barely a whisper. “We can’t test this theory.”

“And why is that?” asked Voskhod.

“Because it would require all Type A Civilizations from the beginning of time to have followed the same model.”

“Which is consistent with the Copernican Principle,” Voskhod nodded. “But is that enough to make the laws of physics, as we know them, testable?”

“That’s a philosophical question,” Baxter scoffed. “But given the unknowns and uncertainties, its impossible to know right now. All we can do is count on future discoveries and hope it all makes sense someday.

Voskhod placed the cap on the dry marker and set it down on the board.

“Exactly. See you in the morning.”



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Matt Williams

Matt Williams

Space/astronomy journalist for Universe Today, SF author, and all around family man!