One of my colleagues just raised a point I hadn't thought of vis á vis Special Relativity.
I had always thought that an observer on a photon would not experience time. My colleague suggests that each frame of reference - the fast moving and the "stationary" - would experience time as "normal" but see the other FoP FoR as having stopped. I don't know enough to be more than mildly dangerous. Can anyone resolve this?
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The truth is that observer on a photon doesn't really make sense....
Real particles -- including, um, us -- are "timelike", in that the sign of their interval is negative (or, if you use the other convention, positive, but in any event it's the same as the sign of the (0,0) term of the Minkowski space metric). A "spacelike" separation are two points in space and time separated by a positive interval. In your frame of reference, the two ends of a ruler at exactly the same point in time is a "spacelike" separation. A spacelike separation means two events (points in spacetime) that cannot be causally connected-- that is, no light ray could connect one event to the other. (A light ray could connect one end of the ruler to the other end... but not one end at t=0 and the other end at t=0 where t is time measured in the rest frame of the ruler.)
To be an observer as we understand it is to have a timelike interval.
Photons have a null interval. Does this mean that time doesn't elapse for them? Dunno... but to have a null interval, you must be massless, and if you are massless, you move along null-interval paths through spacetime.
No matter how much you accelerate, you can never reach the speed of light. YOu are always getting faster, but you asymptote to the speed of light. Nothing that is timelike -- say, you or me -- can become null in special relativity. So, I fear the answer is that the question isn't really a meaningful question.
It's kind of hard to say, but since no observer could travel that fast the point is moot (nothing massive can travel at the speed of light, and any observer would have mass).
In thinking about it, I'm just not sure whether it would even make sense to have an inertial frame moving that fast anyway, since gamma would be infinite [that's 1/(1 - (v/c)^2)^(1/2)], or really non-existent, for everything that you're moving relative to. That whole dividing-by-zero thing is what makes this a real dilemma.
I think that the best way to imagine it would be moving very close to, but not quite at the speed of light. In that case your colleague would be correct, the observer would experience time "normally" and see everything else as nearly at a standstill. Even at the speed of light, the principle of relativity should still hold, meaning that your colleague's interpretation would be right.
But now I'm curious about whether photons "experience" time (whatever it means for a particle to experience anything). I mean in the sense that if they were radioactive, would they ever decay? In my current extremely-tired state I might be missing something or thinking about this incorrectly, but it seems like they never would (since their proper time would be uniformly zero). So in that sense you'd be right, they wouldn't experience time.
But that would fly in the face of the principle of relativity, so something must be up here. I suspect I'm missing a deeper principle (or at least some more-complicated mathematics) to truly analyze this (I'm only a Physics undergrad). I don't think I've been particularly helpful, coming up with an argument for both positions. Hopefully someone with more experience will be able to give a better answer, I think I'd go with "It's a moot question since no observer can go that fast anyway."
This is, of course, a thought experiment, such as the one that inspired Einstein in the first place (what would you see if you were on a tram receding from a clock at the speed of light?). I know we cannot accelerate a real particle to the speed of light. That is irrelevant.
To the previous commenters, ignore going exactly the speed of light. Wilkins' point holds as one *approaches* the speed of light just as well, and this is possible.
The answer is simple: from each observer's perspective, he observes time moving slower for the other one (call this situation I). This seems contradictory but offers no real problem. If, after this situation, the two observer's are brough to move with zero relative velocity (so they are "in the same frame"), then one would imagine a more serious discrepancy (call this situation F). However, to get to situation F from situation I, one observer must be accelerated. Using the dynamical laws of special relativity (i.e., the SR extension of Newton's laws) to describe the effects of acceleration, one finds that both observer's agree on time passed (as they must, being in the same frame) and that they agree that the time experienced by the accelerated observer is longer than that of the unaccelerated observer.
Approaching the speed of light is one thing, but for something moving at the speed of light, there is no conception of time (or space) at all.
I believe that the photon would experience its entire existence along the entire line of its flight all in a "simultaneous" instant so it experiences zero time and sees no time pass in the world. What it would observe assuming it could perceive other photons is whatever photons are crossing its path as it passes, but all at once, so that if it "paid attention" to a single object, different points along its length would see that object as it appeared at different times.
As far as I understand it, a photon "experiences" being created, then instantly reaching its destination. There is no passage of time for a photon. As far as I know.
Flavin and Chris have it right. You can tell because the Lorentz factor (gamma) goes to infinity. There is a thread about this on physicsforums. http://www.physicsforums.com/showthread.php?t=51863
Also, Hartle's Gravitation has a good section on special relativity.
This is essentially a rewording of the twin paradox. Wikipedia to the rescue!
http://en.wikipedia.org/wiki/Twin_paradox
anon#4 has the right approach, imo. Asking "what happens when you travel at the speed of light" will almost always lead you into absurdities. The only correct way to approach this sort of problem is to treat the speed of light as a limiting case.
I had always thought that an observer on a photon would not experience time. My colleague suggests that each frame of reference - the fast moving and the "stationary" - would experience time as "normal" but see the other FoP as having stopped. I don't know enough to be more than mildly dangerous. Can anyone resolve this?
MU!
(As several people have noted, it's a question that makes about as much conventional sense as a Zen koan, so you might as well get a Zen answer...)
Here's an incredibly amateurish observation. To literally see something, you need light to reflect off it and then stimulate your optic nerve. Assuming light could reflect off a photon, for the sake of the thought experiment, wouldn't that light need to be travelling faster than the photon? Light travelling faster than light???
Of course, the other simplistic response is that, unless you close your eyes, you are continuously observing photons.
Ex-drone: no. Relativistic addition of velocities actually gives the velocity as c even if both bodies are moving at c. Again, it's better to think of the limiting case of two bodies moving towards each other at high speed. The relative velocity is
(v1+v2)/(1+v1*v2/c²)
which tends towards c as _either_ v1 or v2 or both tend(s) towards c.
What is baffling to me, as a complete layman, is the notion of a photon which, to an observer, is extended in both space and time - it can start at one point in space and time and travel to another point in space and time - but which 'experiences' no time itself. If the photon is timeless it should be eternal or at least unchanging, yet, apparently, we observe them to to start and end at specific points, both of which would seem to involve changes of state.
Other people have addressed the SR answer (according to SR a photon can't experience time).
But...there is a problem with that answer. And that is that from an external observer's perspective a photon doesn't appear static (as would be implied by SR).
One way of thinking about a photon is as an oscillating electromagnetic field. Energy 'sloshes' back and forth between the magnetic and electric components. This 'sloshing' propogates at the 'speed of light', by definition :).
That's a problem. How can it 'slosh' if it itself does not experience 'time' between its creation somewhere and its absorption somewhere?
There is an apparent contradiction: SR tells us a photon should not experience 'time' as such, observation seems to tell us it experiences "something" that seems to at least have a passing resemblance to 'time' to an external observer (more properly, we are talking about 'interval' and it is composed of both space and time, and the issue is that the interval for a photon is always exactly '0').
I've slipped a fast one in there. The contradiction isn't real.
Points to the person who figures it out. Hint: Think Quantum Mechanics and mathematical limits.
:)
@Ian H Spedding FCD
As a stupid student, my explanations isn't very good, but I'll still try:
A photon is insofar eternal as, as long as no external agent acts on it, it doesn't change ever (in contrast to a radioactive particle which will eventually decay, even with no external influence).
This is intuitive, since when no time passes (for the photon) then there's no time for change.
But if something external acts upon the photon (let's say an electron that absorbs the photon) the photon vanishes instantly (ie. no time required) and the electron acquires the energy from the photon (and probably emits it later again).
Does that make sense?
NO! The whole point of this older thought experiment was that Einstein eventually realized the central premise was impossible. No observer could ever ride on a beam of light because all observers must always measure light to be traveling at c regardless of their reference frame. Asking what he would see while riding on a beam of light was a very fruitful action, but the question itself turned out to be invalid.
It is absolutely relevant. If you're going to ask others for help outside of your personal expertise, you should at least listen to what they say instead of trying to 'correct' them.
The first anon has it off course backwards, the accelerated observer experiences less time not more, as the twin paradox nicely observes. But I still agree with the people who state that it is a meaningless question and it doesn't lead to any insight into relativity. Now on to the topic of energy conservation in GR...
Sitting on a Photon
(A Calypso to be sung to the melody of Sitting in Limbo)
Sitting on a photon
Waiting for some time to pass
Sitting on a photon
Waiting for some time to pass
But does it pass more slowly with a light beam up your arse?
Sitting on a photon
Thinking thoughts of Albert E.
Sitting on a photon
Thinking thoughts of Albert E.
Do I have the time now for another cup of tea?
Sitting on a photon
As the time it comes and goes
Sitting on a photon
As the time it comes and goes
Goes it fast or slowly? Only Albert really knows!
"I had always thought that an observer on a photon would not experience time. My colleague suggests that each frame of reference - the fast moving and the 'stationary' - would experience time as 'normal' but see the other FoP as having stopped."
Errm - what's an FoP?
A way to think about space, time and velocity in SR (cribbed from Brian Greene's Fabric of the Cosmos): Consider a map divided into grids. For a given velocity, movement along the x axis means velocity along the y axis is less (in other words, a car moving directly north at 25 kph goes north quicker than a car moving NE at 25 kph). In SR, an object moving through spacetime will move through time more slowly (time will pass for it more slowly) the faster it moves through space. The sum of velocity through spacetime will always equal c, so for a photon time passes not at all.
Since from Michelson-Morley light is always moving at c relative to any observer, we can deduce that from the "point of view" of the photon, time must pass at "full speed" for any observer, while for any observer, time cannot pass for the photon.
Brandon (#9):
This is a reworking of the twin paradox, and it isn't. If one of the "twins" is a photon, it moves at c relative to any observer by definition. The reverse is also true - if one of the "twins" moves at c, by definition it is a photon, and cannot be an observer (as Caledonian said in a slightly different way).
Where John's interlocutor was getting confused was in mixing the "twin paradox," where we have two observers as well as the question of which moves relative to the other (given that there are no privileged frames of reference for observers), with a scenario that includes a photon, where there is no question as between photon and observer regarding which is considered to move and which is considered stationary.
John S. Wilkins
Caledonian
Acceleration to the speed of light is actually not relevant. Examine the initial premise: "I had always thought that an observer on a photon would not experience time." [Emphasis mine]
In the premise, the observer is already moving at the speed of light. There is no acceleration. Looking at the limiting case is misleading because the behavior at the limit is qualitatively different from the behavior leading up to the limit.
With that being said, I do think the question is ill formed. Asking what happens to an observer going the speed of light is like asking, "What happens when ex does equal zero?" There's no way to ever make it happen, so why worry about it?
Though I guess that's why I'm a physicist and not a philosopher.
FoP should be FoR - Frame of Reference. My bad.
The question is basically whether a photon undergoes time transformation. Ignore massy observers and the physics of observation. It's a legit question if only because Einstein himself posed it.
This comes out of a discussion in that well known textbook, The Science of the Discworld which I lent to my colleague.
Thony, do you have a MIDI file for that song? I'd love to use it in class...
had always thought that an observer on a photon would not experience time
Hmmm, I would think to experience anything requires consciousness :) Which seems very much associated with time and the concept of "now", something that most physicists (including Einstein, I think) never liked to discuss.
As I posted it on your blog I consider it covered by your 'CC' declarations so you are more than welcome to use it. You can find the melody here. The Jimmy Cliff original is beautiful but I was inspired by the Garcia/Grisman "Grateful Dawg" version which is one of my favourite Jerry covers. You have to add strategic pauses to get the final line of each verse to scan. I have added a bridge which goes between the second and third verses.
I haven't had the time now to think this prop'ly through
Since Wilkins put the question, so I wrote this song for you.
If you think you have an answer, then post it on the web
Cause Wilkins is going crazy and its messing up his head
I suggest you get Jason to help you sing it in your class!
"The question is basically whether a photon undergoes time transformation."
Depends upon in what sense you mean "time transformation."
I suppose one could simplistically say time passes slower as you move quicker, and since a photon moves at max speed, it moves not at all in time. (See my comment with the borrowed map-grids example at #20 above.)
But I think transformations should be seen as what happens to objects in space-time so they always maintain the same relation to the invariant photon traveling along at c. There is certainly support in Einstein's writings for this view: http://www.bartleby.com/173/11.html
Thus a photon would not experience transformations of any kind, including the time transformation.
At this point, the best response to the question is to unask it and start over.
There was a young lady from Bright,
Who travelled faster than light.
She went out one day,
In a relative way
And came back the previous night.
An observer implies a memory which of course has a latent write/read time to whatever medium it could use for storage. The photon or any other particle moving at C exists and then does not as it is the carrier of information. The observer can only record the results. Sorry to be cryptic but this is hole in our logic. It does make sense though in equations!
Caledonian:
If the question is unasked, can you be counted on to unanswer it?
Fascinating thread, though I don't understand it all.
I wonder, how would a photon's "experience" change in experiments where light is slowed down to 38 mph?
The first anon has it off course backwards, the accelerated observer experiences less time not more, as the twin paradox nicely observes. But I still agree with the people who state that it is a meaningless question and it doesn't lead to any insight into relativity. Now on to the topic of energy conservation in GR...
As I posted it on your blog I consider it covered by your 'CC' declarations so you are more than welcome to use it
Acceleration to the speed of light is actually not relevant. Examine the initial premise: "I had always thought that an observer on a photon would not experience time." [Emphasis mine]
Steve asked: I wonder, how would a photon's "experience" change in experiments where light is slowed down to 38 mph?
It wouldn't. It's still moving at the velocity of light in that medium, so it does not experience time. It will move at the speed of light with regard to any other non-photon in that medium, no matter the velocity (which can never reach light speed) of the non-photon, so the non-photon will experience the same types of transformations (time dilation, etc.) as would occur in any other medium, while the photon will experience no transformations.
Mr Wilkins if you go here this man's research is the visualisation of what happens when you sit on a photon (i just saw him talking about his work on television) maybe he can answer your question.
Well I think we can never ever travel at the speed of light, only get quite close to it, think the reason if you put a ball next to a grenade, the grenade blew off, the ball would go up to a speed less than that of the exploding stuff in the grenade, if you start a jet engine, you are never going to go faster than the fire (and other stuff lol) coming out of the back of your jet, if you want to go at the speed of light you'll need something that goes faster than the speed of light to get you up to that speed. Maybe a solar sail spacecraft is our only hope possible to get us near to the speed of light.
This is essentially a rewording of the twin paradox.
Here come the girls live with the speed of light.