Is the particular speed of light caused by the PlanckLength?

Discussion of theories involving time as a dimension, time travel, relativity, branes, and so on, usually applying to the "real" universe which we live in.

Is the particular speed of light caused by the PlanckLength?

Postby Eric B » Sat Jan 13, 2018 1:42 am

I had recently been reading on the speed of light, to see if anyone has come up with some idea on why that speed. I had already realized that the speed of light is not an inherent property of light (especially since it can slow down and even stop!) but rather, it’s the maximum speed of "causality". The way I have come to see it, via string theory, is that it's about the spacetime strings themselves. It's basically the effect one string’s energetic (vibrational) state can have on another. I liked the way the PBS “Space Time” video “The Speed of Light is NOT About Light” put it, it’s the fastest speed any two parts of the universe can “[b]talk to each other"[/b].

If light can be slowed down by passing through matter, matter consists of strings in a particular vibrational pattern, according to string theory. But then spacetime consists of strings also. We’re accustomed to thinking of space as “nothing” (especially given terms like “vacuum” and “void”), but it really is “something”. In other words, a “vacuum” is not totally a vacuum; space itself is a kind of “fabric” (after all) according to this theory! Perhaps it’s simply the spacetime strings themselves that limit how fast anything can be propagated/transmitted through them, just like the strings comprising matter reduce the speed further.

So we should then go all the way down to the fundamental units of space and time; the lengths below which reality breaks down:

Planck length=10-35m
Planck time=10-43s
c=10-35m per 10-43s

Each superstring represents one point in space and time. Like it's said that “we can’t ‘drop anchor’ in the universe” and define a definite point in space”; but that’s when plotting by the three coordinates of space only, and leaving time variable. That’s what you can’t do. That then is what you have to take into account relativity, and ask which frame of reference you’re looking at.

According to this idea, a string has no “world line”; it only can be plotted in one “instance” of Planck time. When one instance passes, then it is essentially “replaced” by another string. The location of that string in space of course is determined by the relative frame of reference of the one observing it.

“Speed” is only a determinant of relative change of position in space between two observers. So if you could take all of space, in one instant of time for a particular frame of reference, then two objects will have a definite number of stings between them. If they’re a meter apart, then there will be 100 decillion strings between them, which is 1035. Motion is determined when if in the next instant of time, that number increases or decreases. You can’t determine which object is at “rest” or not, and you may even have differing views of the measured “distance” between them, but there will be a different number of strings, representing a changing distance, as each instant of time passes.

Matter and force “particles” may simply be vibrations passing from one string to the next. Each passing instance of time represents a “move” (think chess/checkers) which could be to an adjacent string in time, or in space, but with a limitation.

So c is perhaps created by two rules:
1) Motion (change of relative string position) can only occur over time (a vibration can only occupy one string per vertical row i.e. space dimension). If time (vertical on the Minkowski diagram) is not traversed, the object is frozen in time and can’t move.
2) Strings in spacetime cannot be jumped over. Motion of vibrations must always pass through adjacent strings.

Either case would then make any trajectory of y<x impossible. That would mean all FTL travel (even if more than 0° to the horizontal on the Minkowski diagram) would actually have a segment of technical infinite speed; being more than one point of space at a time. For a vertical line, you can move through time without moving through space (that is, in your own frame of reference), but then this again is not defined, as other frames of reference will see you as moving.
If for every “move” you must always advance at least one instance of time and stop at every point in space you cross, then the y=x trajectory of coordinate time basically amounts to y=0x in proper time. One string over and one “up” is for all purposes the next one “over” as if you weren’t going up. More than one string over is something that doesn’t exist in your frame of reference for to communicate with that point would amount to being two places at the same time.

So the universe having a "maximum [finite] speed" is tied to it having a minimum [nonzero] length and a minimum duration.

So would anyone say that is a viable explanation?
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Re: Is the particular speed of light caused by the PlanckLen

Postby Mercurial, the Spectre » Sat Jan 13, 2018 4:05 pm

It is related mathematically. Simply, you have the formula:
Planck length = sqrt(ħ*G/c^3).
ħ is the reduced Planck constant equal to 1.054571800*10^-34 J*s/rad.
G is the universal gravitational constant equal to 6.67408*10^-11 m^3/(kg*s^2).
c is the speed of light in a vacuum equal to 299792458 m/s.

I think your argument sounds good, but we don't have a theory of quantum gravity, so it probably sounds conjectural.
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