Does Light Move or Exist Simultaneously in Special Relativity?

[Ravi Prakash]

According to special relativity, for an object (say a photon) moving at the the speed of light, the time taken to travel any distance relative to itself is essentially zero. So in a way, can't it be said that light exists simultaneously in all places ? Or ultimately, does light move at all or does it just appears to move relative to us ?

 

[Khashishi]

That's a question of interpretation, and not something that can be answered by evidence. The invariant interval is indeed zero along a light ray in vacuum. Penrose was working on a concept called Twistor Theory, where each light ray is essentially treated as a point. You could think of light rays as the physical manifestation of two events separated by a null interval "touching". Perhaps one could say that this idea is not even wrong.

 

[Ibix]

https://www.physicsforums.com/threads/infinite-time-and-sr.804030

 

[PeterDonis]

can't it be said that light exists simultaneously in all places ?

No. Even though the arc length along a null curve is zero, the curve still consists of distinct points. You just need to find some other parameter besides arc length to distinguish them. For any light ray, there will be such parameters.

 

[robphy]

In addition, all of those points are causally ordered... That is, there is an invariant sense that one event on the light ray in spacetime is in the future of the preceding events on that light ray.

 

[Ravi Prakash]

That's a question of interpretation, and not something that can be answered by evidence. The invariant interval is indeed zero along a light ray in vacuum. Penrose was working on a concept called Twistor Theory, where each light ray is essentially treated as a point. You could think of light rays as the physical manifestation of two events separated by a null interval "touching". Perhaps one could say that this idea is not even wrong.

What is a null interval ? I tried reading [link to crackpot site removed by mentor], but it was a little confusing. Can you break it down for me ?

 

[wabbit]

What is a null interval ? I tried reading <link removed> , but it was a little confusing. Can you break it down for me ?

The confusion comes from using a poor source.
There is a mention at the top of that page :

this website is not intended to provide educational information about mainstream physics

That is all you need to read from that site.

 

[PeterDonis]

What is a null interval ?

A null interval is an interval along which the arc length is zero. This is possible only because the metric of spacetime, unlike the metric of ordinary Euclidean space, is not positive definite. In ordinary Euclidean space, any two distinct points are always separated by a positive squared arc length, given by (for the simple case of a 2-dimensional Euclidean plane) $ds^2 = dx^2 + dy^2$, where $dx$ and $dy$ are the differences in the $x$ and $y$ coordinates of the two points. You should recognize this as just the familiar Pythagorean theorem.

In spacetime, however, if we consider the simplified 2-dimensional case where one dimension is time $t$ and the second is distance $x$ along one spatial axis, the squared arc length formula has a minus sign in it: $ds^2 = dx^2 - c^2 dt^2$. This means that there are now three different possible kinds of intervals: $ds^2$ can be positive, negative, or zero. The usual names for these three possibilities are spacelike (the interval has positive $ds^2$), timelike (the interval has negative $ds^2$), and null (the interval has zero $ds^2$).

(Note that some sources use a different sign convention, where the squared arc length is given by $ds^2 = c^2 dt^2 - dx^2$. This doesn't affect any physics, but it means the signs of spacelike and timelike intervals are exchanged in the mathematical equations. Null intervals are still zero.)

 

[Ravi Prakash]

In addition, all of those points are causally ordered... That is, there is an invariant sense that one event on the light ray in spacetime is in the future of the preceding events on that light ray.

What do you mean by this ?
#utterly_confused

 

[Ravi Prakash]

The confusion comes from using a poor source.
There is a mention at the top of that page : That is all you need to read from that site.

Thank you, can you suggest a better source ?

 

[PeterDonis]

What do you mean by this ?

He means that, even though the arc length along a light ray is zero (since the interval along a light ray is a null interval), the ray is still composed of distinct points, and there is still a well-defined time ordering to those points; all observers agree on which points are "before" or "after" which others. (In ordinary Euclidean space, we are used to using arc length to determine the ordering of points; but since we can't do that along a null interval in spacetime, it's nice to know that it is still possible to do it.)

 

[Ravi Prakash]

the squared arc length formula has a minus sign in it

Why is there a minus sign ?

 

[wabbit]

Thank you, can you suggest a better source ?

PeterDonis already provided a detailed explanation about null intervals, but for similar questions a good source to check is The Usenet Physics FAQ. Wikipedia articles also often provide good introductions to many topics (e.g. https://en.wikipedia.org/wiki/Spacetime has a section "Spacetime intervals in flat space"). Other than that, there are many good websites about Relativity but I'm afraid I can't think of one right now, sorry - others might have more suggestions. Also, a good source will depend on what you're looking for exactly - and if you want to learn Special Relativity, a textbook might a better option than a website.

Edit : you might also want to try Einstein's book "Relativity : The Special and General Theory" which is full of explanations and not heavy on equations.

 

[PeterDonis]

Why is there a minus sign ?

Because that's how spacetime works; in order to correctly model the results of experiments in relativity, we have to put the minus sign there.

 

[Ravi Prakash]

PeterDonis already provided a detailed explanation about null intervals, but for similar questions a good source to check is The Usenet Physics FAQ. Wikipedia articles also often provide good introductions to many topics (e.g. https://en.wikipedia.org/wiki/Spacetime has a section "Spacetime intervals in flat space"). Other than that, there are many good websites about Relativity but I'm afraid I can't think of one right now, sorry - others might have more suggestions. Also, a good source will depend on what you're looking for exactly - and if you want to learn Special Relativity, a textbook might a better option than a website.

Edit : you might also want to try Einstein's book "Relativity : The Special and General Theory" which is full of explanations and not heavy on equations.

Noted... :)