Introduction:

The very quintessence of human connection, empathy, a facet bedecked with the habiliments of understanding and shared sentiment, stands poised for a potential paradigm shift in a world where technological progression births an "empathy engine." This dialectical exploration embarks upon the intricate trajectory of socio-psychological recalibration engendered by such an advanced technological apparatus, simultaneously scrutinizing the labyrinthine ethical quandaries and multifarious pitfalls poised to traverse the path less taken.

Reshaping Societal Relationships:

The epochal advent of the empathy engine ineluctably portends a kaleidoscopic transformation, from the microcosm of personal interactions to the macrocosm of geopolitical entanglements.

1. Augmented Understanding: The veritable alchemy of technology enables an unmediated transference of emotional experiences, eschewing cognitive chasms that often obscure lucid understanding amidst socio-cultural variances. Empathy, often a laborious endeavor, transmogrifies into an effortless synesthesia of shared emotional hues, curtailing prejudicial preconceptions.

2. Conflict Resolution Redux: The fabric of conflict resolution, warp-tugged by empathetic threads, stands primed for renaissance. As disputants partake in an empathetic pas de deux, veering through each other's emotional vistas, the ethereal choreography could orchestrate resolutions imbued with empathy's mellifluous notes, averting the cataclysmic crescendos of discord.

3. Global Synchrony: On the global dais, leaders and denizens alike could enrobe themselves in the vestments of unfamiliar emotive timbres, fostering the proliferation of international camaraderie. The maelstrom of animosity and estrangement could yield to the siren call of shared human experience, guiding nations toward symphonic diplomacy.

4. Empathetic Activism: The operatic crescendo of societal transformation crescendos as empathetic encounters burgeon into a formidable instrument of activism. The immersion in the tribulations of marginalized cadences catalyzes fervent advocacy, orchestrating societal symphonies that crescendo toward inclusivity and parity.

Challenges and Ethical Quandaries:

Alas, within the interstices of promise, the labyrinthine corridors of ethical turmoil echo. These nascent paradigms teem with resonances of ethical dilemmas and ontological pitfalls, each demanding introspection.

1. Permeable Emotional Precincts: The seamless fusion of emotional terrains, while forging bridges, could also erode the bastions of individual emotional sanctity, precipitating an existential identity crisis as emotional boundaries wane.

2. Informed Ethereal Consent: The unsolicited transmission of emotions stands as an ethical precipice, threatening to unravel the mosaic of emotional autonomy. The clarion call of consent in the realm of empathetic exchanges must resound to obviate unwitting trespass.

3. Emotive Subterfuge: The digital conduits might well metamorphose into malevolent conduits of emotional manipulation, ensnaring unsuspecting souls in webs of emotional artifice, subverting the authenticity of the human emotional spectrum.

4. Empathy Voyeurism: The technology's siren song may lure individuals into the temptations of "empathy tourism," a voyeuristic escapade into the tumultuous seas of others' emotions, eroding the solemnity of genuine emotional engagement.

5. Erosion of Authenticity: The hallowed sanctuary of authentic emotional communion could dwindle as emotions are bartered and shared. The salubrious hum of genuine relationships could recede in the din of borrowed emotional currencies.

6. Cultural Alchemy: Amidst the mélange of emotions from divergent cultural strata, the crucible of comprehension could falter. An amalgamation of emotionally syncretic exchanges risks the flattening of intricate cultural nuances.

7. Sisyphean Reliance: The pernicious shadow of excessive reliance looms, as a society ensnared in the embrace of the empathy engine might relinquish the cultivation of innate empathetic proclivities, stymied by technology's formidable cradle.

8. Emotive Overdrive: The persistent inundation of emotions, ceaseless waves borrowed from diverse quarters, portends an emotional maelstrom. The precarious equilibrium between personal emotions and communal empathies teeters on the precipice of exhaustion.

Conclusion:

The "Empathy Engine" ideation unveils a tapestry where technology and empathy converge, knitting a narrative of amelioration and perturbation. Amidst the chiaroscuro of potential, a symphony of empathy interplays with a cacophony of ethical symposia. It is incumbent upon us to heed the clarion call of ethical prudence, weaving the tapestry with meticulous threads of consent, authenticity, and empathy. In this potent dialectic, the empathy engine beckons as both siren and muse, poised to catapult society into uncharted emotional territories.