u/Shanaki

I've been chewing on the Planck length lately — the ~1.6×10⁻³⁵ m scale where quantum gravity effects are supposed to kick in — and ran into what I think is a genuinely underrated tension that nobody talks about clearly.

The core argument:

If space has a minimum length (Planck length) and time has a minimum tick (Planck time), then you cannot keep adding nines to the speed of light forever. Eventually you hit c. Here's why:

Speed is distance per unit time. Kilometers per second always increases as you accelerate. In smooth spacetime, you can go 0.9c, then 0.99c, then 0.999c, then 0.9999c — you can keep adding nines asymptotically without ever reaching c.

But if there's a Planck floor — a smallest possible length and smallest possible time — then you're working with discrete steps. Each step in space takes one unit of Planck time. You can't subdivide further. So as you accelerate and your speed increases, you're eventually going to run out of nines to add. You'll hit a point where the next increment doesn't give you 0.99999c. It gives you c. There's nowhere in between.

The thought experiment that makes it concrete:

Imagine spacetime as an old film reel crossed with a tile floor. The projector flips frames at a fixed rate — one Planck time per frame. The floor is tiled — one Planck length per tile.

A particle moving through this world can only occupy one tile per frame minimum. It can move 1 tile per frame (speed c), or slower by spacing its jumps: move 1 tile every 2 frames (0.5c), move 1 tile every 10 frames (0.1c), and so on. You can approximate 0.9c, 0.99c, 0.999c by choosing longer and longer spacings between your tile jumps.

But here's the critical part: you can only keep doing this if you have infinite frames to work with. The moment you run out of frames — or the moment the spacing gets so fine that you're trying to subdivide a single frame — you're stuck. You can't add another nine. The next increment is c. Full stop. No asymptote. Just a wall.

Why we don't observe this:

We measure particles going 0.9999999c in accelerators and cosmic rays. The Lorentz factor gamma follows its equation perfectly all the way up. No jumps. No quantization. No ceiling at some subluminal speed.

So either:

1. The Planck length and Planck time don't actually exist as fundamental minimums, or
2. Spacetime is smooth, not discrete.

Because if there is a discrete floor at Planck scale, with space and time both quantized together, then special relativity's smooth asymptotic approach to c is impossible. One of them has to break.

The additional bind (relativity makes it worse):

Even if you try to save discrete spacetime by making the grid "abstract" or "relational," you run into another problem. Special relativity says moving observers see lengths contract. If the Planck tile is supposed to be the smallest possible length, but a fast-moving observer sees it shrink, you've violated the definition of "smallest." You can't have an absolute minimum length that's also frame-dependent. That's contradiction.

So a truly fixed grid contradicts relativity. But a grid that contracts with your motion isn't fundamental anymore — it's not a floor, it's a mirage.

What current physics says:

• The naive "spacetime is a grid" picture is dead. Ruled out by 100+ years of relativity tests.
• Whether spacetime has some Planck-scale structure that avoids these traps is still open: causal sets (random point clouds), loop quantum gravity (discrete area/volume spectra), or smooth spacetime with quantized gravity fields are all still live proposals.
• None of them are settled. This is an honest open problem, not something we've solved.

The real constraint: any theory claiming discrete spacetime has to explain why velocity doesn't quantize, or accept that the discrete floor is so far below detection that spacetime is empirically indistinguishable from smooth.