An Impossible Particle May Somehow Fit Into General Relativity After All,

A straightforward math tweak could bring tachyon fields into line with the rest of physics.
Tachyons are faster-than-light particles, and tachyon fields are special cases of quantum field.
The math adjustment enlarges a tiny Hilbert space into a larger one to accommodate variables.

In a fascinating twist of theoretical physics, scientists may have calculated how an elusive particle, the tachyon, could exist without breaking the laws of general relativity.

Theoretical models involving missing pieces and parameters often posit new, exotic particles as a way to close their gaps. But these models are complex, including ranges and likelihoods of other parameters. When a team of scientists can sharpen one of those parameters, the new particle can move closer to or further away from existing and conforming to physics as we know it.

Theoretical physicists live in a world the rest of us can’t really understand. They identify phenomena from the far-out cosmos, including things that don’t make sense to our Earth-centric mindset, then they flesh out a model using all the things we can roughly calculate. A tachyon is a particle that travels faster than light (superluminal), which is considered impossible. And a tachyon field, therefore, is something that doesn’t fit into our current understanding.

Tachyon fields have long been “the enfant terrible of physics,” these scientists explain, but recent work has continued to move them from outlandish toward, maybe, merely implausible. Now, this team is adding another update to keep moving tachyon fields toward plausibility. Their work appears in the peer-reviewed American Physical Society journal Physical Review D.

The key, they explain, is in doubling one of the parameters in today’s understanding of tachyon fields. The Hilbert space is a working model used in complex mathematics. When describing quantum fields in general, a Hilbert space model with just one particle is enough. In fact, it constrains the math in a way that makes the whole calculation work, because the one particle is never subtracted from or added to. But for tachyon fields, the math is different and must be represented by two intersecting fields instead of one field of just one particle, the scientists say.

That’s because Hilbert space that depicts a tachyon field has to have enough room for a tricky mathematical switch. In our understanding of working spacetime, there’a a series of calculations, the Lorentz transformations, that need to be possible in order for a particular idea to be plausible.

Think of it like any other set of qualifications. If you want to apply to be part of a list of squares, you must have exactly four sides of equal length and exactly four right angles. Without those qualifications, you’re simply another kind of shape. To be plausible in our world, you must be Lorentz compliant, with the equivalent of four sides and four right angles.

If the tachyon field math is constrained to a Hilbert space of just one side, or input, then the Lorentz transformations don’t have room to fully express. That’s because in the course of these transformations, the input and output fields can switch and create an outcome that doesn’t fit into the Hilbert space anymore. The right space, the scientists explain, must be paired of all inputs and all outputs together. That means they can switch back and forth without moving out of bounds.

It’s complicated stuff—but so is cosmology. And despite the heady details, what results is simple: this larger Hilbert space removes the three largest remaining obstacles in our understanding of tachyon fields as part of the same play space as quantum field theory in general.

This, the scientists explain, comes after previous work showing that tachyons are not impossible, but rather more like “disturbances of causality.” Other scientists have also shown that the math of superluminal particles may not be impossible after all.

At one time, physicists were sticking their necks out over the idea of quantum mechanics in the broadest sense. Heck, before that, scientists had to risk their livelihoods to suggest that atoms existed at all, then that subatomic particles existed. Perhaps in years to come we’ll all accept tachyon fields as a building block of our world, with fine-tuned detectors for those as well as dark matter and the other theoretical materials around us. All it takes is a slightly larger working space.

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