Do photons remain stationary in the fourth dimension?
Do photons age?
I've always been interested in that question, but I don't think there's much of an answer because you can't consider the reference frame of the photon itself.
Does QFT have anything more substantial to say?
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.
Photons are fascinating to me. Example, as far as I know, photons do not exist when not moving.
And that a photon goes from zero to c instantaneously is equally fascinating, as I thought that nothing could go faster than c. "Instantaneous" is certainly much faster than c.
Much for me to ponder and learn...
well, we can take the limit i suppose
as v approaches c, time slows more and more.
so at 99.9999% the speed of light, t would be very slow.
so at 99.99999999999999999% the speed of light, t would be very, very, very slow.
and at 100%, it will have stopped, i would imagine.
the velocity of all objects through spacetime is c.
so if an object is moving at c through the three spatial dimensions, its velocity in the fourth dimension is 0.
and vice versa.
brian green talks about this in the elegant universe.
does anyone know the passage or have the book?
please let me know! :)
Photons are truly amazing! I want to talk about a few details here because I hear them a lot.
1) Photons don't "go from zero to c." They just start out at c, continue at c, and end at c :)
Which ties in to what you said at first: you can't have a photon that isn't moving [at c].
2) You're mixing up acceleration, and velocity. Moving from one point to another instantaneously would mean infinity velocity (faster than c). Accelerating from zero velocity to non-zero velocity instantaneously (although it brings up other serious issues--like infinite force, etc) is very different, and has nothing to do with the speed of light per se.
Hope that helps :)
I think the idea is great, but the math is very different. There's a huge difference here between the speed of light, and arbitrarily CLOSE to the speed of light. Its the same difference as between a black-hole, and just a really big star.... the math gets angry at certain values :P
I find this to be one of the most intriguing ideas in physics, and It feels like the kind of thing that might have deep meaning that no one has yet uncovered.
If you consider energy loss with the expansion of space to be "aging"... maybe... but the FAQ is already deeper than that.
I am curious to hear (read) how do you deal with refraction, created either by material medium or by gravitational (general relativity) effects.
It seems reasonable in these contexts to think of photons accelerating.
Photons always move at c. Velocities less than c for an electromagnetic wave are the velocities of the wave formed by the superposition of the incident wave and waves reemitted by the charges oscillating in the medium.
I think it is an elegant way to see how this things work. But let me check one thing:
If this is true then if you put a large (1 m thick) slab of glass in front of a photon source, and set a photo-detector after this slab, then you would be able to measure time intervals consistent with c velocity of propagation from the source to the detector, as the main wavefront is always present.
Nope. The wave pattern does propagate at less than c in the glass. It's just not valid to interpret this as the velocity of photons.
So you see difference between EM field and photon. Is it?
In case you see this difference, do you think photon can accelerate?
Our telescopes receive photons that are upwards of 10 billion years old. That seems to indicate they do not age.
According a NASA release found here: http://science.nasa.gov/science-news/science-at-nasa/2002/27mar_stoplight/ photons can be stopped.
Regarding the tests on light to coerce it to be a wave or a photon: I wonder if any has been done in a medium where the lights travels significantly slower than the standard speed?
If they're 10 billion years old, how do they not age? :P
What does it mean for a photon to age in the first place? For a radioactive sample, I would say you measure age in terms of decay, for a photon... what? What is there to age in the first place, when they are bound to a set speed at all times in a given medium?
For something to actually age, it needs to have an internal structure that can change with time. No elementary particles do, so they can't really age.
For something to really experience the passage of time (or anything else), it needs to be conscious. Things without internal structure certainly can't be conscious.
What we mean when we say that an object or a particle "experiences X" is that in the coordinate system that the standard synchronization procedure associates with the object's world line (or its tangent), some sequence of events is described as "X". That's how the term "experiences" is defined in the context of special and general relativity. The problem is that the standard synchronization procedure doesn't work for null geodesics, i.e. for the curves that can be world lines of massless particles. So the term "experiences" is undefined for photons.
The word "certainly" seems to be inappropriate as we don't even know how to define consciousness. And it seems also to be quite risky to assume that the consequence of a particle not having internal structure is its being unable to present complex behavior. It is more a question of words here, as I agree in general with the estimatives you presented.
In our experience we have only found consciousness associated with complex structures, and it is reasonable to assume that billiard balls and photons are not conscious in any sense that the word is usually used.
My claim is that you can of course say that it is reasonable, but you have no basis to infer that with certainty, at least within the scientifical domain, taken in the sense of natural science.
Something that isn't capable of storing information can't be considered conscious, and a physical system that doesn't have distinguishable states can't store information.
An alectron for instance has spin, and therefore allows one to store 1 qbit. How much information (classical information) can be stored in 1 qbit. Do you know?
Would it be fair to infer from this that Relativity is an incomplete theory?
No, not at all. I don't know a definition of the word "incomplete" that would make SR incomplete, except of course "incomplete"="isn't an exact description of all phenomena", but with that definition, all theories are incomplete. SR is as complete as a theory can get.
I googled and found at least one person who claimed that the answer is "infinite", so I assume that this is what you had in mind, but I would say that this claim is false. I assume that it comes from the fact that the set of spin-1/2 states can be mapped bijectively onto a sphere. Since there are infinitely many points on a sphere, you could argue that there are infinitely many states that the system can "be" in. But it's not at all obvious that a state can be said to represent the particle's properties. The only thing we can be sure of is that it represents the properties of an ensemble of identically prepared systems.
I respect your view of QM. I was just trying to convince you not to use so many certainties. But if you think so, It is OK. For instance, when you said "SR is as complete as a theory can get". Your statement makes one think you have a large experience in investigating completeness of physical theories, for it is a complex field, with so many subtleties. But you certainty is there, talking out loud. If you inserted at least somehing like IMO, it would have sounded better. Or...
Perhaps you do have such astonishing expertise in dealing with philosofical aspects of theories in natural sciences.
But let us focus in some objective debate.
Separate names with a comma.