Is the speed of light a paradox?

[gregorygregg1]

If observed time approaches 0 at the speed of light, does that mean the distance one travles at the speed of light is infinite? Since speed = distance/time, does this mean that, at the speed of light C= infinity/0 which = 0? There then appears to be no speed at the speed of light. Does this also mean that at the speed of light the universe appears to be two dimensional, since the dimension in the direction light travles collapses to 0?

 

[silmaril89]

Nothing with mass can travel at the speed of light. If it could it's possible that some of the strange behavior you are claiming could be possible, but that's probably why it's not possible to travel the speed of light.

 

[SprucerMoose]

If observed time approaches 0 at the speed of light, does that mean the distance one travles at the speed of light is infinite

Isn't there a length contraction missing here? I would say, and I could be wrong, that speed (in fast frame) approaches 0/0, not infinity/0.

 

[Naty1]

yes, the speed of light is a paradox...downright wiered!

Since speed = distance/time, does this mean that, at the speed of light C= infinity/0 which = 0?

Keep in mind that from the perpective of an observer traveling at c, distance in an outside stationary frame is foreshortened and approaches zero, just as the passage of time outside appears to approach 0...but 0/0 still is rather "paradoxical" to our everyday way of thinking.

And physics has a LOT more such paradoxes in store...'The more I learn the less I know."

Foe example, just what is "space" (distance) and what is "time",,,,nobody knows! So the fact they are "paradoxical" should not be a surprise.

 

[silmaril89]

I have before thought of a similar idea to the one you are expressing. Correct me if I'm wrong, but are you asking if in the reference frame of a photon, the distance it can travel is infinite?

Well, I think the answer is...maybe. I don't think anyone really knows, I don't see why it's not possible. But it's certainly nothing we could ever measure, no one could ever be in the rest frame of a photon. So, maybe a photon is able to travel infinitely far in it's own frame of reference, but as far as we are concerned in our frame of reference it travels at the speed of light.

In other words, although it's a cool idea I don't think it really makes much sense to think of it, because it really doesn't matter either way.

 

[gregorygregg1]

yes, the speed of light is a paradox...downright wiered!



Keep in mind that from the perpective of an observer traveling at c, distance in an outside stationary frame is foreshortened and approaches zero, just as the passage of time outside appears to approach 0...but 0/0 still is rather "paradoxical" to our everyday way of thinking.

And physics has a LOT more such paradoxes in store...'The more I learn the less I know."

Foe example, just what is "space" (distance) and what is "time",,,,nobody knows! So the fact they are "paradoxical" should not be a surprise.

I was thinking from an inside perspective. Traveling at 60 miles per hour I would percieve a mile to be one sixtieth as long as someone traveling 1 mile per hour, even though the actual dimension of a mile doesn't change. As a photon at the speed of light I would pass an infinity of mileposts in 0 time. Doesn't that mean dimension collapses at the speed of light? What does this do to the dimensionality of the universe at light speed? Paradox is a mind game. Your move.

 

[Drakkith]

Our math breaks down in the frame of reference of a photon. According to science, a photon does not have a frame of reference. This is because a frame of reference is one where the observer is traveling at 0 velocity. Light cannot do that and therefore has no frame.

 

[shawn1990]

since mass, length and time is proportional to motion, does that mean length, mass and time on Earth is different than on say jupiter, pluto?/?...

 

[silmaril89]

I believe that would be correct. If Jupiter is moving relative to the Earth (which it is), observers on Earth and observers on Jupiter will disagree on certain events on earth.

 

[yuiop]

Seeing as how this thread is slightly philosophical I would like to offer the following casual thought. Let us say we a long horizontal string and induce a wave at one end. The disturbance propagates along the string to the far end, but no atoms or molecules of the string actually move horizontally along the string. The same principle is true for a wave in the open ocean. The wave propagates horizontally for hundreds of miles, but the individual molecules just move a short distance up and down. The point is that waves can have the property that energy can be propagated without involving the movement of anything with mass in the same direction. So if we consider light as a wave, then nothing actually moves at the "speed of light", just the propagation of a disturbance. (In this case we would have to use Lorentz Ether Theory which is mathematically identical to SR but philosophically different.) Asking for the point of view of photon then becomes pointless, because it is like asking for the point of view of the disturbance that propagates along the string or across the ocean.

 

[Arens]

Seeing as how this thread is slightly philosophical I would like to offer the following casual thought. Let us say we a long horizontal string and induce a wave at one end. The disturbance propagates along the string to the far end, but no atoms or molecules of the string actually move horizontally along the string. The same principle is true for a wave in the open ocean. The wave propagates horizontally for hundreds of miles, but the individual molecules just move a short distance up and down. The point is that waves can have the property that energy can be propagated without involving the movement of anything with mass in the same direction. So if we consider light as a wave, then nothing actually moves at the "speed of light", just the propagation of a disturbance. (In this case we would have to use Lorentz Ether Theory which is mathematically identical to SR but philosophically different.) Asking for the point of view of photon then becomes pointless, because it is like asking for the point of view of the disturbance that propagates along the string or across the ocean.

Thanks for this post. You answered some questions i had in my mind about light.

 

[bcrowell]

Asking for the point of view of photon then becomes pointless, because it is like asking for the point of view of the disturbance that propagates along the string or across the ocean.

I agreed with everything up until here. I don't see why it's logically impossible for a traveling wave pattern to be conscious. Arguably you and I are traveling wave patterns, since we're made out of things like electrons, which are waves. I don't see why mass transport is relevant. Actually, a box full of light waves has rest mass due to the light, so if you move the box around, you're performing mass transport by moving the light.

IMO the reason you can't have observers who travel at c is purely relativistic, and any explanation that doesn't use relativity isn't an explanation.

Below is my own attempt to give a coherent explanation of why you can't have observers traveling at c.

-Ben

FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn't possible, but let's be more explicit. There are two possibilities. The velocity V of the system's center of mass either moves at c, or it doesn't. If V=c, then all the particles are moving along parallel lines, and therefore they aren't interacting, can't perform computations, and can't be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer's frame of reference isn't moving at c. Either way, we don't get an observer moving at c.

 

[alphali]

u can't talk about time in general u must put a frame of reference . let's say that a spaceship was able to travel at speed of light and u as an observer from outside u can calculate the distance traveled if u know that he is moving at the speed of light by multiplying the speed v by time t(measured by ur clock) but if u where able to look at the pilot u will see that he is frozen in time not aging u will look at his clock and see that it stopped. but also he can claim that he is stationary and u are moving( jut like looking at the trees or people on the road while driving the car ) so when he looks at ur clock he will see it stopped .for him his clock is moving normally and he can calculate how much he traveled by multiplying his speed by time(measured by his clock).now u might say who is really aging and who is not , who is traveling at the speed of light and who is not ? well the only answer to that is from whose perspective

 

[harrylin]

If observed time approaches 0 at the speed of light, does that mean the distance one travles at the speed of light is infinite? Since speed = distance/time, does this mean that, at the speed of light C= infinity/0 which = 0? There then appears to be no speed at the speed of light. Does this also mean that at the speed of light the universe appears to be two dimensional, since the dimension in the direction light travles collapses to 0?
[..]
I was thinking from an inside perspective. Traveling at 60 miles per hour I would percieve a mile to be one sixtieth as long as someone traveling 1 mile per hour, even though the actual dimension of a mile doesn't change. As a photon at the speed of light I would pass an infinity of mileposts in 0 time. Doesn't that mean dimension collapses at the speed of light?

I'm not sure to understand all your questions. Anyway, here you obviously talk about the limit which never can be reached. And with that understanding, Einstein mostly answered your questions - IMHO correctly - in 1905:

For v=c all moving objects—viewed from the “stationary” system—shrivel up into plane figures. For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.

- http://www.fourmilab.ch/etexts/einstein/specrel/www/