We’ve talked about why physics sometimes produces infinities, but let’s make it tangible with three famous examples: black holes, the Big Bang, and electrons. Each shows how the assumptions in our models can push beyond reality — and how relational thinking helps us understand what’s really happening.
1. Black Holes: When Spacetime Collapses
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The classical picture: General relativity predicts that at the centre of a black hole, density and curvature become infinite.
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What’s really happening: Our model treats spacetime as a perfectly smooth continuum and sometimes even treats the mass as concentrated to a point.
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Relational perspective: Nature can’t support distinctions at infinitely small scales. The singularity isn’t a literal “point of infinite density” — it’s a signal that our theoretical cut is too sharp. We’re asking for a level of detail spacetime doesn’t have.
Think of it like this: trying to divide a droplet of water into infinitely smaller drops — eventually, the notion of “drop” loses meaning.
2. The Big Bang: When the Universe Gets Too Small
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The classical picture: Extrapolating backwards, the universe shrinks to a point of infinite energy density at t = 0.
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What’s really happening: The FLRW model treats the universe as a perfectly uniform fluid with a smooth, continuous spacetime. At very early times, these assumptions break down.
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Relational perspective: The “singularity” is a warning light. The distinctions our model tries to make — energy density at an infinitesimal point in time — are finer than the relational potential of the universe.
Imagine trying to measure the temperature of a single atom using a thermometer designed for oceans. The measurement becomes meaningless.
3. Electrons and Point Particles: When Zero-Size Becomes Problematic
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The classical picture: In quantum field theory, electrons are treated as points interacting with continuous fields.
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What’s really happening: Fields blow up at the location of a point particle, producing infinite self-energy.
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Relational perspective: Isolating a particle from its relational context is an overly narrow cut. Infinity shows that the model is asking for distinctions that the system can’t support at that scale.
Picture it like trying to balance a lightning bolt on the tip of a needle. The math can describe it, but reality doesn’t have a tip that small.
The Common Thread
In all three cases:
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Idealisations (smooth spacetime, homogeneous fluids)
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Point particles (zero-size, over-localised objects)
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Ignoring fundamental scales (Planck length/time)
…lead to divergences not because reality is infinite, but because our cuts — the distinctions our models impose — exceed the relational potential of the system.
Why Quantum Gravity Matters
Quantum gravity isn’t just a “fix” for equations. It’s about recalibrating our cuts:
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Spacetime may be discrete or “grainy” at the Planck scale.
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Particles may be extended objects rather than dimensionless points.
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Models become aligned with what the system can meaningfully sustain.
Infinities vanish not because the math changes, but because the model no longer asks for impossible distinctions.
Bottom Line
Whether it’s black holes, the Big Bang, or electrons, infinities are informative signals, not physical catastrophes. They tell us: “You’re trying to see more than what the system allows. Slow down, adjust your perspective, and make your cut align with reality.”
Physics is not just a measurement tool — it’s a way of construing reality. Singularities, divergences, and infinities are the system’s way of teaching us the limits of our view.
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