Is Space Infinitely Divisible?

[snap360]

Hello all,

A friend of mine (physics major) recently told me that light exists outside of time. Is this true? Doesn't make any sense to me but I only know what popular science tells me.

Thanks

 

[cristo]

What do you mean by "light exists outside of time?" In what context did he say this; i.e. what discussion were you having?

 

[snap360]

What do you mean by "light exists outside of time?" In what context did he say this; i.e. what discussion were you having?

He was suggesting that since light exists outside of time, it is reasonable to think that God can do the same. Does this context make any difference? It seems that he could have an argument in that any moving body "exists outside of time" relative to stationary bodies? Or am I wrong with that?

 

[coalquay404]

And he's a physics major? Who's trying to argue for the existence of God based on a flawed understanding of physics?

Hmm.

 

[theCandyman]

Since it takes time for light to travel a given distance, doesn't that completely contradict the claim that light is outside of time?

 

[Integral]

From the frame of reference of a photon, neither time nor space exists.

Unfortunately his argument does not hold water. If god exists in the same frame of reference as a photon... Wouldn't the gods be debating our existence rather then us debating gods existence?

 

[ktoz]

From the frame of reference of a photon, neither time nor space exists.

Wouldn't that imply that the universe only requires a single photon? If there's no space or time from a photon's frame, then to it, all matter exists in the same space at the same time. There would be no need for more than one photon as it wouldn't need to "move" at all to perform all the electromagnetic work required of it.

If there is no space or time from a photon's frame then, for it, the universe is indistinguishable from a black hole.

This seems rather strange...

 

[pervect]

We've had this discussion before, several times

One standard web reference:
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html

Several past threads
https://www.physicsforums.com/showthread.php?t=132528
https://www.physicsforums.com/showthread.php?t=107741&page=2
https://www.physicsforums.com/showthread.php?t=105484Time Dilation Question

It's basically an error to attribute the usual sort of reference frame to an object moving at the speed of light.

If one has some basic knowledge of the concept of the Lorentz interval, it is easy to see why. The Lorentz interval between any two points of the worldline of an ordinary observer is timelike. Thus such an observer experiences time along their worldline. The Lorentz interval along any two points of the wordline of a photon is null. A null interval is neither timelike, nor spacelike. Thus a photon does not experience "time in the same sense that a person or any object made out of matter does. To assume that it does is basically an example of the anthropormorphic fallacy, to give human characteristics to something that is not human.

Interestingly enough, it does turn out to be possible to mark out "regular intervals" along the worldline of a beam of light. For instance, imagine a beam of light of constant frequency. This beam of light has a wavelength, and the peaks and nulls of this wavelength (or of the electric field) mark out "regular intervals".

A more technical way of approaching this same topic is to talk about parameterizing the geodesic of the worldline of a photon by an affine parameter. Only linear transformations of the affine parameter are possible without changing the structure of the geodesic equations. In some sense, then, we can talk about 'even spacing' of points by 'even spacing' of this affine parameter.

Taking this idea further and going along with it, one can (using the arbitrary coordinates possible in General relativity) build a coordinate system for a photon - a coordinate system where three of the coordinates of the photon are fixed, and one coordinate represent At least one of the coordinates (the one along the photon's worldline) must be null. (One of the more symmetrical coordinate systems has two null coordinates and two space coordinates).

So a photon doesn't experience time, but in some abstract sense it "experiences" a null coordinate - at least, one can distinguish regular intervals along a photon's worldline. But in spite of the fact that these intervals are regular in some sense, they should not be confused with time. The intervals are not timelike - they are null intervals, neither timelike nor spacelike.

 

[robphy]

So a photon doesn't experience time, but in some abstract sense it "experiences" a null coordinate - at least, one can distinguish regular intervals along a photon's worldline. But in spite of the fact that these intervals are regular in some sense, they should not be confused with time. The intervals are not timelike - they are null intervals, neither timelike nor spacelike.

Let me add the comment that a photon does experience a causal order [which does not rely on any notion of regularity]. That is, a photon could in principle experience event A, then a different distinct event B, etc... even though no proper-time is ticking away for the photon.

 

[ktoz]

If one has some basic knowledge of the concept of the Lorentz interval, it is easy to see why.

I read your links and also your explanation of the Lorentz interval https://www.physicsforums.com/archive/index.php/t-67731.html" and one thing strikes me as not automatically obvious or true. Namely, the Lorentz interval assumes that space is infinitely divisible because the Pythagorean formula

$$sqrt(x^2 + y^2 + z^2)$$

can yeild values that have an irrational distance. Is it really reasonable to suppose that distances "in the real world" can be irrational? It may be that the problem of infinitely divisible space has been thoroughly explored but I've never run across it in my hobbiest level readings.