Lithium atom ‘wave packets’ were the subject of an article in the New Scientist this week, and were imaged. I’m not commenting on the article, just running with the concept of viewing wave packets as a fundamental unit to see where it might go
What might cause one wave packet to bind with each other? I’ll assume, for discussions sake, “particles” are simply coherent, structured wave packets—modes—whose behaviour is not governed by imposed fields, but by internal coherence and mutual anchoring.
Take two such wave packets, \psi_1(x) and \psi_2(x), each defined by a coherence density \rho_i(x) and a phase field \phi_i(x). Their internal structure is stabilised by a anchoring costs, which we may write for a single packet as:
B[\psi_i] = \iint \rho_i(x) \Gamma(x - x{\prime}) \rho_i(x{\prime}) \cos\left[ \phi_i(x) - \phi_i(x{\prime}) \right] \, dx \, dx{\prime}
Here, \Gamma(x - x{\prime}) is the anchoring kernel—a positive, real function governing the spatial coherence coupling between regions. When this integral remains below a critical threshold \varepsilon_i, the wave packet retains coherence; if exceeded, the mode decoheres, disperses, or transitions.
two wave packets could anchor or bond to one another if a mutual coherence link forms
The simplest mutual anchoring cost functional between the packets \psi_1 and \psi_2 is:
\mathcal{C}_{12} = \iint \rho_1(x) \, \Gamma(x - x{\prime}) \, \rho_2(x{\prime}) \cos\left[ \phi_1(x) - \phi_2(x{\prime}) \right] \, dx \, dx{\prime}
This is an interference-weighted overlap integral. It quantifies how well-aligned the two wave packets are—not just in space, but in phase. If the integral is large and negative, they are in antiphase and tend to destabilise one another. If large and positive, they are phase-aligned and mutually reinforcing.
Mutual anchoring—and hence binding—is energetically favoured when \mathcal{C}_{12} is negative and decreases the total system cost. That is, the two modes together are more stable than apart.
The total anchoring energy for the pair becomes:
\mathcal{C}\text{total} = B[\psi_1] + B[\psi_2] + \lambda \, \mathcal{C}{12}
with coupling strength \lambda > 0 setting the sensitivity to mutual coherence. Binding occurs when:
\Delta \mathcal{C} = \mathcal{C}_\text{total}^{(\text{bound})} - \left( \mathcal{C}_1^{(\text{free})} + \mathcal{C}_2^{(\text{free})} \right) < 0
That is, the combined configuration is more coherence-efficient than the sum of isolated ones.
This framework explains not just classical “attraction”, but coherence-driven phenomena like:
- Formation of composite particles
- Decay via de-anchoring
- Spin exclusion (when the cosine term turns negative from phase antisymmetry)
- Even modal resonance bonding (when small shifts in phase alignment sharply lower \mathcal{C})
So, mathematically, two wave packets bind together when their shapes overlap and their internal wave rhythms are in step. If this happens, the cost of maintaining their structure— the “effort” required to keep them stable—is lower together than apart.
There is no need to imagine a force field between them; they remain close simply because it is easier for them to remain coherent as a pair than alone.
I’d expect such a concept to be expandable so that mass and gravity could emerge. It could be fun
I don’t know how to format equations in the chat. Is it markdown or latex or what