# How can light move?

1. Sep 2, 2015

### Fowler

If a photon travels at the speed of light it will appear as if it's time has stopped. But if it's time has stopped how can it move?

2. Sep 2, 2015

### Staff: Mentor

In relativity the fact that the spacetime interval between two events is 0 does not imply that the two events are the same. This is a difference between Minkowski geometry and Euclidean geometry.

3. Sep 2, 2015

### bcrowell

Staff Emeritus
Saying that a photon's time has stopped is not really correct. Relativity doesn't have frames of reference moving at c, so it's not possible to define how fast time passes for a photon.

A better way to look at it would be to imagine an observer, say a person in a spaceship, moving very close to, but not exactly at, c, relative to the earth. They might be able to travel from hear to Alpha Centauri in 5 minutes of their time, which according to an observer on earth took them 4 years. The observer aboard the spaceship explains this as being because the distance from our solar system to Alpha Centauri was length contracted from 4 light-years to 5 light-minutes.

4. Sep 2, 2015

### Staff: Mentor

Even if it were correct to say that time is stopped for light in SR, it wouldn't imply that the light can't move. Much of the point of SR is that elapsed time (and distance) in one frame doesn't have to match the elapsed time in another.

5. Sep 3, 2015

### pervect

Staff Emeritus
I'd say the underlying issue here is the usual one, the stubborn and prevailing notion of "absolute time" that we inherit from Newtonian mechanics. How to solve this problem is much less clear, abstract discussion of the perils of believing in absolute time seem to do little good. Most likely, this is due to a combination of factors, including how closely held the belief in absolute time is, the difficulty of imagining that things could possibly be otherwise, the abstract nature of the discussion, and the difficulty in appreciating even the relevance of the whole issue until it is properly understood.

Techniques suggested for use in the classroom (i.e. Scherr et al paper , "The challenge of changing students deeply-held beliefs about the relativity of simultaneity" don't seem to me to be all that effective in the different context of discussions on PF, though it's hard to be sure.

[add]Let's see if I can do a little bit better at showing at least the relevance of the issue. The underlying idea being disucssed is the idea that "time stops". But what does this mean? I believe that the usual (and incorrect) picture of "time stopping" that motivates the OP's question is the notion that clocks slow down and eventually stop when compared to the imagined notion of "universal time", a notion of a sort of time that everyone agrees on and that pervades the universe. But the real issue is that there is no such universal time that pervades the universe. Sinceit doesn't (and can't exist in the context of Special relativity, being incosistent with the theory) , it's impossible to compare clocks against it!

Last edited: Sep 3, 2015
6. Sep 3, 2015

### bcrowell

Staff Emeritus
I'm not convinced that this is the fundamental underlying issue -- or maybe it's one of the underlying issues for some people, but it's not the main one or the only one. It is perfectly possible to formulate in a formal way this naive notion that "time stops if you go at the speed of light." It can simply be taken as a statement about the limit where the mass of a clock approaches zero while its mass-energy remains constant. I think the issues involved when people ask this question are:

(1) possibly a naive belief in simultaneity, as you say

(2a) not realizing that there are no frames moving at c

(2b) OR, in the formulation I gave above, not realizing that the limit of a frame of reference is not necessarily a frame of reference itself

(3) Not reasoning correctly about Lorentz transformations. E.g., the OP in this thread seems to have been imagining that time dilation would make motion slow down, so that infinite time dilation would make motion stop.

7. Sep 4, 2015

### A.T.

It's speed is defined by a clock at rest, which isn't slowed down.

Last edited by a moderator: Sep 4, 2015
8. Sep 6, 2015

### Staff: Mentor

I think this is an important point. The action of Lorentz transformations on timelike vectors is fundamentally different from their action on null vectors; timelike vectors get rotated (hyperbolically), while null vectors get dilated. The whole "time is stopped for a photon" thing implicitly assumes that Lorentz transformations act the same way on null vectors as they do on timelike vectors, so it breaks down once you realize the actions are different.

9. Sep 8, 2015

### Fowler

So this seems that this has been the least disagreed on answer, and if I'm understanding it correctly you mean:
Just because something is not moving along the spacetime axis it does not mean it cannot move though the first 3 dimensions.

But then how come light isn't just everywhere always then?

10. Sep 8, 2015

### Staff: Mentor

Your original question asked how can light move if time is stopped for it. Obviously, coordinate time is not stopped in our reference frame and our proper time is not stopped either, so you are clearly asking about something else. There is no reference frame for light, so you cannot be asking about the coordinate time of the light. So that leaves the proper time of the light. Proper time is equal to the spacetime interval along a timelike path. Light travels along a lightlike path, so the spacetime interval along a light path should not be called proper time, but nevertheless the interval itself is well defined and is 0 along the path of light.

So basically, the only way that I can see to understand your question in a way such that it has a meaningful answer is to assume that you are asking how light can travel if the spacetime interval along its path is 0.

In Euclidean geometry, this would be a correct objection. We draw a spacetime diagram and we say that something "moves" if it is represented on the spacetime diagram by a worldline, where the slope of the worldline is related to the speed of the movement. If spacetime geometry were Euclidean, then two points with zero interval between them would be the same point, so they would not define a line, just a point. So a path like that would be just a single event and indeed could not be said to move. However, in Minkowski geometry you can indeed have two events which have 0 interval between them but are not the same event, and those events can define a worldline, and the slope of such a worldline is a speed of c in all frames.

In Euclidean geometry, the locus of points which are a fixed distance from the origin is a sphere. Different distances correspond to spheres with different radii. The locus of points which are 0 distance from the origin is a degenerate "sphere" which is the single point located at the origin.

In Minkowski geometry, the locus of events which are a fixed interval from the origin is a hyperboloid. Different intervals correspond to hyperboloids with different vertexes. The locus of events which are 0 interval from the origin is a degenerate "hyperboloid" which is a cone centered on the origin. This cone is called the light cone. It is a well-defined locus that does not cover "just everywhere always".

Last edited: Sep 8, 2015
11. Sep 9, 2015

### Staff: Mentor

Closed pending moderation.

Edit: Thread reopened. Many off topic or incorrect posts have been removed.

Last edited: Sep 9, 2015
12. Sep 25, 2015

### cyc454

Hi Fowler! I think you can find the part of the answer in the pattern below (sorry but I had to use it, it is very useful and not so long :) ) :
Small prelude:
$s'= s \sqrt{1-\frac{v^2}{c^2}}$, where $s'$ is the distance measured in "moving" ref. frame (lets say your bro ref. frame), and $s$ is a distance in, lets say, your ref. frame. If something is moving really fast in your ref. frame (so $v$ is big ) the right side of the equation (so also left side) become small. So lets say your bro was moving with $v=0.9c$ and lets say he traveled 1km in your ref frame. In his ref. fame it was much shorter distance according to equation above. So, for $v=0.999999999999999999999999999999999c$ he traveled REALLY short distance in his ref. frame. But He didn't feel the slowdown of time lapse in his ref. frame (I am talking here about rate, not about difference in measured values of time coordinate in two different ref. frames!)! He measured the $t'$ in his ref. frame much shorter than you ($t$) because the $s'$ for him was short (according to equation above). End of prelude ;)

Now how about light? Well, the problem is that we don't know what will happen for $v=c$ because the equation above was derived on the assumption that $v \ne c$ (for $v=c$ denominators in some fractions during deriving becomes 0---not good! :) ). But you saw that for $v$ almost equal $c$ your bro travelled almost 0km in his ref. frame. So if $v$->$c$, $s'$-> $0$. But time lapse does not slowdown in "moving" ref. frame (your bro will not feel any changes in time lapse rate). Only the distance and duration of travel become shorter in his ref frame.

13. Sep 26, 2015

### Jim Hasty

Einstein said, "Keep it simple - but not too simple." The question of "How can light move?" The simple answer is "This cannot be defined for several reasons: (1) in spacetime there are three world-lines: timelike (where we live), spacelike, and null (neither timelike nor spacelike); light exists in the null region. (2) Light has zero mass and is never at rest, so it has no rest frame, which means an observer riding on a light beam (if that were possible) could not make any observations about the universe around him; massive observers (which have rest frames) can observe light, but light cannot observe the universe. That is a good question but difficult to answer.

14. Sep 26, 2015

### vanhees71

Yes, let's keep it simple. It is an empirical fact that light is an electromagnetic wave, and it is very well described by Maxwell's equations. Maxwell's equations are nothing else than a classical relativistic field theory of a massless vector field (which necessarily is a gauge field). These equations describe electromagnetic waves, which move with a phase velocity of $c$, which is (because the field is massless) precisely the limiting speed of relativity. This implies that there is no reference frame, where the phase velocity of electromagnetic waves vanishes. Relativity was discovered by accomodating the empirical fact that the speed of light is the same in any reference frame, and not dependent on the relative motion between the observer and the light source.

Now, it is not so clear to me, what the OP wanted to ask, because he used the word photon. It's NOT off-topic to stress again, that photons are no point particles, and there is no way to intepret the correct notion of photons in terms of QED as such. Perhaps something what comes close to the naive idea of a photon is a wave packet for a classical electromagnetic wave. A plane electromagnetic wave in the vacuum travels also with the limiting velocity $c$ (at least approximately, where the group-velocity, $\partial \omega/\partial k=c$ is applicable as the speed the center of momentum of the wave packet is moving.

15. Sep 26, 2015

### VALENCIANA

I love Jim Hasty´s explanation.

16. Sep 30, 2015

### Jorgelff

How a photon "see" the world around it?

17. Sep 30, 2015

### Mister T

I think the difficulty in understanding lies with the notion of relative time. If you had a space ship orbiting Earth at almost the speed of light it would experience time passing much more slowly relative to us. People aboard the space ship would experience time just the same as if they had remained here with us.

The faster the speed of the space ship the larger the effect, so naturally we want to extrapolate and say that time would stop if the space ship were traveling at the speed of light. When we learn that's not possible we wonder what would happen for something that could do it, like a photon. Speaking loosely, a photon can't experience time. Just a couple of decades ago we thought that neutrinos might travel at the speed of light and realized that if they did they wouldn't be able experience time. And if that were true they wouldn't be able to change into another kind of neutrino when traveling from, say, the sun to Earth. We now have established that they have mass and they travel at speeds less than the speed of light, so they can and do change types.

It might be better to think of the speed c as the maximum possible speed rather than the speed of light. Some day we may discover that photons have mass and travel at a speed just under c. If that were to happen c would then become known as the limiting maximum speed that nothing material can ever achieve. Like absolute zero is the limiting low temperature that can never be achieved. The theory of time slowing, which by the way is now a well proven fact, won't change at all. We'll just call c the maximum possible speed rather than the speed of light. And it'll retain its value of exactly 299 792 458 m/s.

18. Oct 1, 2015

### weirdoguy

It's meaningless to say that photon sees anything, because there is no reference frame of photon.

19. Oct 1, 2015

### ZapperZ

Staff Emeritus
So you and your friends decided to play a game of basketball. You are playing along merrily, scoring points left and right, when another person wanted to play but then asked "Hey, if I were to just climb the basketball ball post, sit behind the backboard, and then someone from below keeps passing me basketball that I can then just easily dump through the basket, how many points do I get for each basket?"

If that happens, what you would say? If it were me, I'd say that (i) you are awfully strange because the game rules doesn't allow you to do that and (ii) this is no longer a basketball game that we all know and love, and you have invented a new game. So you have to come up with a new set of rules.

Let's get this VERY clear: When you invoke ideas such as "time dilation" (as in claiming that time has stopped for a photon), or asking what a photon "see", you are already invoking a very clear and stringent set of rules as set upon by Special Relativity. Period! There's no negotiating. And one of the "rules of the game" set by SR is that the speed of light in vacuum is a constant for ALL inertial reference frames.

What this means, and what one of FAQ has already stated, is that our physics that resulted in all these "time dilation" etc. started from such a premise, and it also means that these rules cannot be applied to a frame in which light is at rest! This is because in such a frame, the foundation of SR is no longer true, and you can't simply use the same set of rules and apply them to where they can't be used! So by claiming and asking what the physics would be like if you are at c, you are also claiming that you can violate SR and you are inventing a "new game and a new set of rules". We don't know yet if there is such a thing as "time dilation", or even if time stands still at c, because there's no valid description for such a scenario.

So, if you wish to know what SR would predict or say under such-and-such situation, you have to, first and foremost, be aware of its restrictions and its "rules of the game". Otherwise, you are sitting on the backboards and dunking your basketball. You may be fine with it, but it is no longer the known basketball game.

Zz.

20. Oct 1, 2015

### vanhees71

The only difference between the basketball game and physics is that in the former case you are free to invent new rules and create a new game, but in the latter case this doesn't work, because physics is about describing (quantitatively and as precisely as possible) what's going on in nature. Nature doesn't care about, which rules you like, but you have to discover the laws valid in nature, and relativity is the result of centuries of research figuring out such laws. You never know the validity of the so found laws, but you have to carefully check them by comparing them to observation. Up to now relativity always has been right in predicting the outcome of all observations, and there is no reason to abandon any of the laws described by it. This implies that it simply doesn't make sense to ask how the world looks from the restframe of a photon, because according to these laws there doesn't exist such a rest frame (let alone that photons are no point particles in any usual sense, but that's another story).