Correlated Spacetime: A New Approach to Quantum Gravity — A Fun Exploration using AIs

Authors: Rajesh Bhaskar, GPT-4, Claude AI

### Exploring Nature with AI

I tried this fun exercise with GPT-4 and Claude AI, where I threw in an idea that space and time are actually correlated and not separate dimensions as such and would ask each AI to propose the full theory. Then I take content from one AI and put it to the other, expanding on the concept. Here is the output from the conversations with my “colleagues” GPT-4 and Claude AI. Both of them seemed to think it was a fascinating and innovative approach and actually proposed some mathematical formalisms. BTW, I am not a physicist (though I have an MS in Chemistry) but this seemed like fun, so take it for what it is worth.

### Start of conversation

I started off by asking GPT-4 the following:

Rajesh: Imagine a spacetime where space and time are very strongly correlated instead of being separate dimensions. How we can tell time if f there is no change in spatial coordinates of any particle in the system. Or how we can tell distance between points in space if there is no time. Hence the correlation.

GPT-4: In some ways, you could argue that space and time are already correlated. Change over time often involves change in spatial coordinates: the ticking of a clock, the rotation of the Earth, etc. Without change in spatial coordinates, it would indeed be very difficult to measure or perceive the passage of time. And on the other hand, without time, distance becomes a moot point, as there’s no “when” for the “where” to take place.

The correlation you’re referring to seems to go beyond this, though. You’re suggesting a type of universe where space and time aren’t just correlated but are inseparable to such an extent that one cannot exist without the other. This idea challenges the conventional understanding of space and time as distinct dimensions.

This would result in a unique spacetime, where any change in spatial coordinates would necessarily correlate with a change in time and vice versa.

I passed on the same content to Claude AI, and then back to GPT-4.

And so on.. Here is the output from this exercise, recreated for an internet audience, as a Medium article.

### Introduction

The quest to unify quantum mechanics and general relativity — our best descriptions of the micro and macro universe respectively — has been a longstanding challenge in theoretical physics. Both theories have been immensely successful in their respective domains, yet they remain incompatible when it comes to situations where gravity becomes strong on quantum scales, like black holes or the Big Bang. To reconcile this discord, a novel perspective is necessary. A promising approach that my colleagues and I are developing is the “correlated spacetime theory.”

### Motivation

Quantum mechanics brought forth the revolutionary idea of entanglement — a phenomenon where particles, no matter how far apart, can be instantly correlated with each other. This suggests a deep-level interconnectedness in the universe, prompting us to look beyond the traditional notion of local causality.

General relativity, on the other hand, showed us that space and time aren’t rigid and distinct entities but rather dynamic aspects of a single spacetime fabric.

Inspired by these, our approach seeks to carry these connections further by suggesting that the spacetime fabric itself is intrinsically interlinked — not just space with space and time with time, as in Einstein’s spacetime, but also space with time.

### The Correlated Spacetime Hypothesis

In our correlated spacetime theory, we take a bold step beyond Einstein’s revolutionary spacetime concept. Rather than seeing space and time as different aspects of a unified backdrop, we posit that they are fundamentally interconnected. This correlation between space and time at each point in spacetime is the bedrock of our theory.

We introduce additional off-diagonal terms to the spacetime metric tensor, the mathematical object in general relativity that encodes the spacetime geometry. These terms represent the correlations between space and time and modify the standard geometry of spacetime. They imply that the presence of matter-energy not only curves space and slows time, as in general relativity, but also entangles space and time, producing new physical effects.

### Implications and Predictions

The correlation of space and time leads to novel physical effects and offers an exciting way to reconcile quantum mechanics and general relativity. The notion of quantum entanglement becomes less mysterious if space and time are fundamentally interconnected. The causality puzzle in quantum mechanics, where measurements can instantaneously affect distant particles, may find a natural explanation in the context of correlated spacetime.

This theory also implies a quantized spacetime — the so-called “spacetime foam” at the Planck scale. This might resolve the issue of infinities that plague quantum field theory models and offers a fresh perspective on the unification of quantum mechanics and general relativity, potentially leading us to a theory of quantum gravity.

### Key Aspects of Correlated Spacetime Theory

Here are some key bullet points highlighting core aspects of the correlated spacetime theory:

• Fundamentally recasts spacetime as an intrinsically correlated fabric rather than independent dimensions
• Space and time intervals are proposed to be deeply interlinked in a non-trivial manner
• The metric tensor of general relativity is extended to include off-diagonal terms that couple space and time coordinates
• Einstein’s field equations are modified to incorporate interaction between spatial and temporal metrics
• Matter particles are modeled as quantized, stable excitations of the correlated spacetime itself
• Quantum fields arise from disturbances or fluctuations within the spacetime fabric
• A spacetime hypervolume measure unifies spatial and temporal differentials into a 4D entity
• The invariant speed of light naturally emerges from the coordinated spacetime structure
• Intrinsic properties like mass and charge arise from geometrical characteristics of stable spacetime excitations
• Quantum entanglement can be explained by linked excitations of the correlated spacetime
• Spacetime correlation provides a pathway to unify quantum theory and general relativity
• At appropriate scales, the theory reduces to the predictions of quantum mechanics and general relativity
• Causality is subtly modified by off-diagonal metric terms while retaining overall arrow of time
• The spacetime hypervolume provides a natural cutoff for calculations, addressing renormalization challenges
• Opportunities exist to extend black hole and cosmological solutions within this framework
• Further mathematical formalism development and experimental testing required to fully establish viability

### Future Steps and Challenges

Our theory is still in its nascent stage. Developing a complete mathematical framework for correlated spacetime and finding solutions that describe realistic scenarios like black holes or the early universe are formidable tasks ahead of us. Despite the challenges, the potential insights and solutions offered by the correlated spacetime theory make it a promising direction in the pursuit of quantum gravity.

### Conclusion

The pursuit of understanding the fundamental nature of the universe has led us from viewing space and time as absolute and separate entities to envisioning them as aspects of a single, malleable spacetime fabric. Our correlated spacetime theory is the next leap forward, suggesting an intricate, deep-seated connection between space and time. While this is a radical departure from the established view, it is the kind of revolutionary idea that might just hold the key to unifying quantum mechanics and general relativity and unraveling the true quantum nature of the universe.