# Simple thought Experiment, Straight Line between 2 Distant Points

1. Dec 2, 2014

### ricardo81

(from my limited understanding)

In our observable universe a photon could travel say, 5 billion light years in a straight line if unperturbed. Call the points X and Y travelling down-up.

If point X was moved one Planck length to the left, would it still be able to travel exactly to point Y?

2. Dec 2, 2014

### DaveC426913

Are you asking of the universe is a fixed, pixelated grid at the Planck level?

i.e. would the photon have to "jog" to the left?

No.

Imagine a Planck unit was the size of a 12"x12" floor tile, and imagine the photon is a cardboard box 12" on a side. I want the box to go from tile (X1,Y1) to tile (X2,Y99).

There is nothing preventing the box from moving directly from one point to the other. The Plank tiles do not confine the XY position of the photon box; they do not force it to fill one tile and only one tile.

The box occupies an area that is on Planck length on a side at all times, but, unlike kitchen tiles, Planck units are not physical things that stack shoulder to shoulder in an array.

Last edited: Dec 2, 2014
3. Dec 2, 2014

### ricardo81

I guess I am assuming pixelation, or perhaps whether there is a potential limit in the directional freedom of travel. My maths is not the best so I can't put a number to the degrees of that angle.

4. Dec 2, 2014

### Chalnoth

If the universe were simply pixelated, it would violate relativity, and those violations would be observable. There are reasons to believe that space-time is discretized in quantum gravity, but it can't be a regular grid.

5. Dec 2, 2014

### ricardo81

Understood

Understood

Thank you for replying. I worked it out to be something of the order of 7.4945e-59 Degrees ... I guess I had a misconception about planck lengths somehow being used as indivisible units.

My reason for wondering was whether there could have potentially been parts of the observable universe (in regards to metric expansion and light speed) that could potentially be undetectable if there were such a limit to the angle.

6. Dec 2, 2014

### vin300

I disagree with Dave. Photon is a point object. A path of light in non euclidean space is most probably curved, because if it isnt it must have exactly zero curvature. If it is indeed straight, it can still connect the two points with a slight aberration. For the latter, you have two options:1.relative velocity 2.lensing. Lensing may be done optically or gravitationally.

Last edited: Dec 2, 2014
7. Dec 2, 2014

### DaveC426913

Yes, but you're missing the point of the question.

The OP was essentially wondering if the Plank length is a grid. i.e. that, to go from X1Y1 to X2Y99, any target would have to, at some point, make a discreet jog from X1 to X2.

8. Dec 2, 2014

### ricardo81

So I can reasonably assume that every point in a horizon is reachable from every other point?