Highly suppressed detection probability of the primordial antimatter in the present-day universe

This paper proposes that the observed matter-antimatter asymmetry in the current universe is not due to a fundamental lack of primordial antimatter, but rather results from its highly suppressed detection probability caused by the Dirac-Feynman-Stueckelberg interpretation and the extreme time-asymmetric expansion of the early universe.

The Gist

The Great Cosmic Mystery: Where Did All the Antimatter Go?

Imagine the Big Bang as a massive explosion that created the universe. According to our best physics theories, this explosion should have created matter and antimatter in perfectly equal amounts. Think of it like a bakery that bakes exactly 1,000 chocolate cakes (matter) and 1,000 vanilla cakes (antimatter).

But when we look at the universe today, we only see chocolate cakes. We see stars, planets, and us—all made of matter. The vanilla cakes seem to have vanished. For decades, physicists have been trying to figure out where the antimatter went, assuming it was destroyed or that the universe just made more matter than antimatter from the start.

This paper proposes a different, mind-bending idea: The antimatter didn't disappear, and the universe didn't make more matter. Instead, we just can't see it anymore.

The Time-Traveling Wave Analogy

To understand why, we need to look at how physicists (specifically Dirac, Feynman, and Stueckelberg) interpret antimatter. They suggest a very strange rule:

• Matter (like electrons) is a wave that moves forward in time, just like us.
• Antimatter (like positrons) is a wave that moves backward in time.

Imagine you are walking forward down a hallway (Matter). Your friend is walking backward down the same hallway (Antimatter). In a normal, static hallway, you would eventually bump into each other.

The "Stretching Rubber Sheet" Universe

Now, imagine that hallway isn't static. Imagine the universe is a giant, stretchy rubber sheet that is expanding incredibly fast.

1. The Matter Wave: You (the matter) are walking forward. As you walk, the rubber sheet stretches ahead of you. You stay right there in the "present" universe, filling up the space as it grows. You are easy to find because you are right here, right now.
2. The Antimatter Wave: Your friend (the antimatter) is walking backward. But here is the kicker: because the universe is expanding so fast, the "past" is shrinking rapidly behind them. As they try to walk backward, the rubber sheet is stretching so violently that they are being pulled deeper and deeper into the tiny, hot, dense past.

The "Flashlight in a Fog" Metaphor

The authors use a concept called a "propagator" to calculate the chance of detecting these particles. Let's use a flashlight analogy:

• Detecting Matter: Imagine you are shining a flashlight (a detector) into a room to find a person. The person (matter) is standing right in the room with you. The light hits them easily. The probability of seeing them is 100%.
• Detecting Antimatter: Now, imagine the person you are looking for (antimatter) is walking backward into a room that is shrinking and getting smaller every second. By the time you shine your flashlight, they have already walked so far back into the "past" that they are now in a tiny, microscopic corner of the universe that existed billions of years ago.

Your flashlight beam (our current detection methods) is too wide and too "present-day" to catch a particle that has retreated into the microscopic past. The "overlap" between your light and their location is almost zero.

The Math Made Simple

The paper does some complex math to prove this, but the result is surprisingly simple:

• The chance of detecting a primordial electron (matter) is normal.
• The chance of detecting a primordial positron (antimatter) is suppressed by a massive factor related to how much the universe has expanded.

If the universe expanded by a factor of 10 during the time these particles were created, the chance of finding the antimatter drops by a factor of $10^6$ (one million). If you look at the whole history of the universe, that number becomes astronomically small.

Why This Changes Everything

This theory is exciting because it solves the mystery without needing to invent new, undiscovered laws of physics.

1. No "Missing" Antimatter: The antimatter is still there, but it's hiding in the "deep past" of the universe, effectively invisible to us.
2. It Fits the Rules: It explains why we see more matter than antimatter (Sakharov's conditions) without needing to prove that the universe made more matter than antimatter in the first place. It's not that the universe was biased; it's that the "antimatter side" of the equation is mathematically impossible to detect in our current expanding universe.
3. It's Model-Independent: This works regardless of the specific details of the Big Bang. As long as the universe is expanding and antimatter moves backward in time (according to quantum mechanics), the antimatter will be "lost" in the past.

The Bottom Line

The universe isn't a place where matter won the fight against antimatter. It's a place where matter stayed in the present, while antimatter ran backward into the past.

We don't see antimatter today not because it was destroyed, but because it has retreated so far into the shrinking, hot early universe that our modern detectors simply cannot reach it. It's like trying to catch a fish that has swum back into a river that dried up a billion years ago. The fish is still there, in the history of the river, but you can't catch it in the dry bed of today.

Technical Summary

1. Problem Statement

The fundamental mystery addressed is the matter-antimatter asymmetry in the present-day universe. Standard cosmology posits that the Big Bang created matter and antimatter in equal amounts. However, observations show the universe is dominated by ordinary matter.

• Current Status: The prevailing explanation relies on the Sakharov conditions (baryon number violation, C/CP symmetry violation, and thermal non-equilibrium).
• Limitations: Despite decades of research, laboratory experiments have found CP-violating effects orders of magnitude too small to explain the observed asymmetry. Furthermore, extrapolating laboratory physics to the primordial universe is problematic due to the vastly different space-time structures (e.g., extreme time asymmetry and strong gravitational fields) in the early universe, where CPT theorem guarantees may not hold.

2. Methodology

The authors propose a paradigm shift: the asymmetry is not due to different production rates of matter and antimatter, but rather a massive difference in their detection (scattering) probabilities in the present-day universe.

• Theoretical Framework:

  • Dirac-Feynman-Stueckelberg Interpretation: Antimatter is treated as particles with negative energy propagating backward in time, while matter (positive energy) propagates forward in time.
  • Space-Time Metric: The authors utilize the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric for a spatially flat universe. They define a specific coordinate system $(T, \vec{X})$ where $\vec{X} = a(T)\vec{x}$, separating cosmic expansion ($a(T)$) from local particle motion ($\vec{x}$).
  • Approximation: During the hadron and lepton epochs, the expansion rate is fast but the scale factor change over local interaction times allows the space-time to be approximated as locally Lorentzian.

• Mathematical Approach:

  • The authors solve the Dirac Equation using the Feynman Propagator ($S_F$).
  • They calculate the scattering probability amplitude for a primordial particle (electron) and a primordial antiparticle (positron) to be detected in the present-day universe.
  • The calculation involves integrating the propagator with incoming plane waves, accounting for the time direction of propagation ($+\tau$ for matter, $-\tau$ for antimatter) and the expansion of the universe scale factor $a(T)$.

3. Key Contributions

• Reinterpretation of Asymmetry: The paper argues that the "missing" antimatter is not destroyed or never created; rather, its wave function propagates backward into the extremely small, hot early universe, making its overlap with present-day detectors negligible.
• Model Independence: The suppression mechanism is derived directly from the fundamental nature of the Dirac-Feynman-Stueckelberg interpretation and the expansion of the universe. It does not require new physics, exotic CP-violation mechanisms, or quantum gravity effects.
• Resolution of Sakharov Conditions: The authors demonstrate how their model naturally satisfies the Sakharov conditions:
  • Baryon/CP Violation: Interpreted as the suppression of detection probability for antibaryons rather than a difference in production.
  • Thermal Non-Equilibrium: Achieved because particle and antiparticle wave functions move in opposite time directions, reducing their interaction and annihilation probability as the universe expands.

4. Results

The core mathematical result is the derivation of the detection probability amplitudes ($A$) for matter and antimatter:

• Primordial Matter (Forward Time):
  The amplitude for a primordial electron detected at time $\tau$ is calculated. The cosmic scale factor $a(\tau)$ cancels out during the integration of the momentum space.
  $$A_{elec} \propto \text{Finite value (independent of } a(\tau) \text{)}$$
  The matter wave function fills the present-day universe, allowing for significant overlap with detection waves.

• Primordial Antimatter (Backward Time):
  The amplitude for a primordial positron (propagating backward to time $-\tau$) involves the scale factor at the time of "creation" relative to the time of "detection." Because the universe was much smaller in the past ($a(-\tau) \ll a(0)$), the amplitude is suppressed by the ratio of the scale factors cubed.
  $$A_{posi} \propto \frac{a^3(-\tau)}{a^3(0)}$$
  Consequently, the detection probability (proportional to $|A|^2$) is suppressed by a factor of:
  $$P_{posi} \propto \left( \frac{a^3(-\tau)}{a^3(0)} \right)^2$$

• Quantitative Example:
  Using the lepton epoch ($\tau = 10$ seconds) where the universe expanded by a factor of 10 ($a(0)/a(-10) = 10$), the detection probability is suppressed by a factor of $10^{-6}$. For the full history of the universe, this suppression is astronomically large, rendering primordial antimatter effectively undetectable today.

5. Significance

• Explains Observational Reality: The paper provides a mechanism for why we observe a matter-dominated universe without needing to invoke unobserved, massive CP-violation in the early universe.
• Unifies Quantum Mechanics and Cosmology: It successfully integrates the time-asymmetric interpretation of antimatter with the time-asymmetric expansion of the universe, suggesting that the "fate" of antimatter is determined by the geometry of space-time.
• Experimental Implications: It suggests that searches for primordial antimatter (e.g., antiprotons from the Big Bang) are fundamentally futile not because they don't exist, but because their quantum mechanical probability of interacting with present-day matter is vanishingly small due to the expansion of the universe.
• Theoretical Economy: The solution relies on established physics (Dirac equation, FLRW metric, Feynman propagator) rather than speculative new particles or forces, offering a parsimonious explanation for one of physics' greatest puzzles.