According to Einstein's theory of relativity, the more speed something has the slower that time passes for it; and presumably when traveling at the speed of light, time stops entirely. So this means that when a photon is created, the rest of existence virtually pauses until the photon ceases to exist, and then the rest of existence begins again. If time is stopped while the photon exists, then what are we measuring when we measure light? In order to measure the actual photon, we would need to take the measurement while time was standing still. Speed requires time, so why do we say that light travels at a speed?
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$\begingroup$ Time dilation is a relative phenomenon, in your question you seem to ignore the notion of a frame of reference. Light travels at a speed, which is fixed in any frame of reference. The ``frame of reference'' of the photon doesn't exist. $\endgroup$– fqqCommented Jul 15, 2014 at 14:16
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$\begingroup$ What do you mean that the frame of reference of the photon doesn't exist? Because the photon is not an 'observer'? $\endgroup$– Derek RobertsCommented Jul 15, 2014 at 14:20
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$\begingroup$ Just that there is no rest frame for photonos. See physics.stackexchange.com/questions/16018/… $\endgroup$– fqqCommented Jul 15, 2014 at 14:25
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7$\begingroup$ Claim: There are no frames of reference where a photon is at rest (i.e. there are no frames travelling at the speed of light.) Proof: The speed of light is constant in all frames. In the hypothetical photon frame, the speed of the photon is 0, yet its speed is the speed of light. Contradiction Thus, there are no frames in which a photon is at rest. $\endgroup$– ACuriousMind ♦Commented Jul 15, 2014 at 14:25
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1$\begingroup$ The speed of light can only ever be approached. It doesn't really make sense to try to understand how a photon experiences the passage of time, because photons are integral to the way that time is defined. $\endgroup$– KidElephantCommented Jul 15, 2014 at 14:25
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3 Answers
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It's simpler than you think. When we measure the velocity of light we are simply measuring how much distance light travels per second. For example if we send a very short laser pulse to a reflector on the Moon and wait for it to return we find it covers the 768,934 kilometer round trip in about 2.56 seconds. This is measured in the Lunar Laser Ranging Experiment.
You're quite correct that time dilation tends to infinity as the relative velocity tends to $c$, but we don't care what's happening in the rest frame of the fast moving object. When we measure a velocity we measure the time in our frame and the distance in our frame.
answered Jul 15, 2014 at 14:42
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$\begingroup$ I like your answer, but *if the theory of relativity is correct, and *if the photon does not experience the passage of time, *then light doesn't travel a distance "per second". Instead what is happening is that the photon is traveling while the observer is relatively frozen in time, and then what the observer measures once the photon is destroyed, is more like the "tail" of the photon than the photon itself. $\endgroup$ Commented Jul 15, 2014 at 14:51
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$\begingroup$ Or in an analogy, the photon splits time and creates visible light similar to how lightning splits the atmosphere and creates thunder. $\endgroup$ Commented Jul 15, 2014 at 14:59
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8$\begingroup$ @DerekRoberts: the rules of relativity say that it's not legal to look at things from a photon's perspective. That insight is one of the things that actually enabled Einstein to formulate the theory. $\endgroup$ Commented Jul 15, 2014 at 15:02
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1$\begingroup$ @JerrySchirmer well $#!+... $\endgroup$ Commented Jul 15, 2014 at 15:03
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If I (on the Earth) and you (on a very fast rocket) measure the time that takes you to travel a certain distance we would not agree. Still, nothing forbids me to compute your velocity using my measures of time and distance. The interesting point is that if your rocket is made of photons, even a third person trying to chasing you will agree with my measured speed. This happens because of the combination of time dilation and length contraction (the person moving with respect to me sees a shorter distance, but his time also goes slower, both of the same factor $\gamma$), he will always agree with me unless he reaches your photonic speed somehow braking relativity. That is just how relativity works: time is not absolute, speed of light is!
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$\begingroup$ If my rocket were made of photons, when it was caused to exist, you and me and the person chasing me would all become frozen in time, and the photon rocket would run the course of it's purpose, and then it would cease to exist, and then time would continue after the photon was gone, and all you would see is visible light rippling through time behind the photon rocket, so how would you measure the photon rocket? You're only measuring visible light, not photons. $\endgroup$ Commented Jul 15, 2014 at 15:50
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$\begingroup$ The time would just cease to exist only for you into your rocket. But who cares of you? You are too fast, both I and the third person measure the same speed and that's enough for us. (You can also "measure" single photons, especially at high energy) $\endgroup$– DarioPCommented Jul 15, 2014 at 15:59
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$\begingroup$ But once time ceased to exist for me, in my rocket, you are no longer able to measure, me or my rocket, because we no longer exist in your time. You can only measure my exhaust, because my exhaust is left behind, in your time. But me and my rocket, we don't exist in your reality anymore. $\endgroup$ Commented Jul 15, 2014 at 16:06
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$\begingroup$ For example, you might make an observation of where I started, and then make an observation of where I ended, and then calculate the distance between the points and the time that you observed me taking to travel that distance, and you come up with a velocity. But, since I existed outside of time, I could have traveled an infinite distance to infinite points in existence between the points where you observed me beginning and ending, because I would have made the entire trip and been at my destination while you were still observing me at my start point. How could you possibly know what happened? $\endgroup$ Commented Jul 15, 2014 at 16:15
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$\begingroup$ If you were able to measure me, you would measure that I was all three, I would be at the start point, I would be covering the entire length of the distance, and I would be at the end point, all in your single measurement. So you wouldn't be measuring my speed over a distance, you would be measuring my length over an infinitely small unit of time. $\endgroup$ Commented Jul 15, 2014 at 16:48
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what are we measuring when we measure light?
When considering "(average) speed of light (in vacuum)", or rather primarily: "(average) speed of a signal front" this means the quotient of
the distance of a signal source and a receiver between each other (i.e. under the condition that these two participants had been at rest with respect to each other), divided by
the duration of the signal source from its signal indication, until its indication simultaneous to the reception indication of the receiver (or equally the duration of the receiver from its indication simultaneous to the signal indication of the source, until it's (the receiver') reception indication).
By the definition of (how to measure) distance between two participants who were and remained at rest with respect to each other as $$c/2 \text{ ping duration},$$
where $c$ is foremost some symbolic parameter which is distinct from Zero,
therefore the value of the "(average) speed of a signal front" can be directly calculated and obtained as $1 ~ c$; or for short: $c$. (That is to say there is no reasonable measurement involved at all, but the result value is obtained as a theorem.)
According to Einstein's theory of relativity, the more speed something has the slower that time passes for it;
That's an unfortunate, imprecise, improper statement. Let's better say that geometric and kinematic relations between participants (such as speed, or curvature) must be accounted for, in order to compare their individual durations to each other.
The details of how to carry out such comparisons can of course be derived; beginning with comparisons between participants who move "uniformly" (straight, and with constant average speeds) with respect to each other. As a consequence, some non-zero value of duration can not be attributed to a signal front "itself".
Addendum:
To address the title question:
Why do we say that light travels at a speed?
Strictly, we don't say that "light travels", which might suggest some particular "path, or curve" being "travelled along"; but rather that signals had been "exchanged" (between some particular source and receiver), without any further presumption of geometry, but in order to establish geometric relations (involving that source and receiver, and perhaps additional identifiable participants) in the first place.
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$\begingroup$ Neil deGrasse Tyson: "As you travel faster, or if you find yourself in the vicinity of a higher source of gravity, time ticks more slowly for you then for those who are not". $\endgroup$ Commented Jul 16, 2014 at 5:02
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$\begingroup$ The speed of the signal front is not the same as the speed of the photon. The speed of the wake is not the same as the speed of the boat. So, you set up your experiment to measure photons. You have all the equipment ready to gather data. You press "start". In that same single moment when you create the photon that you are attempting to measure, the photon that you have created also ceases to exist. Then the experiment begins, and all the data is gathered. But the photon is gone already. So what you're measuring is not light, it's the aftermath of light. $\endgroup$ Commented Jul 16, 2014 at 5:09
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$\begingroup$ Derek Roberts: "How do you account [...]" -- As far as I understand your comment (which, since I first read it, has been removed) the only "accounting" is pretty much summed up in the derivation of the factor $\sqrt{1 - \beta^2}$, which requires (or presumes) mutually equal determination of the value $\beta^2$. The determination of $\beta^2 = 1$ is only unilateral, since signal fronts don't exchange signals between each other, therefore signal fronts cannot be said "being at rest to each other" (or constituting an "inertial frame"), etc. $\endgroup$ Commented Jul 16, 2014 at 5:14
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$\begingroup$ You measured the disturbance that the photon created by traveling through time. $\endgroup$ Commented Jul 16, 2014 at 5:17
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$\begingroup$ Derek Roberts: "So, you set up your experiment [...] In that same single moment when you create the photon that you are attempting to measure, the photon that you have created also ceases to exist." -- No. The "moment" ("indication") of the sender stating a signal is not the same as the "moment" ("indication") of the detector observing that the signal had been stated by the sender (a.k.a. the detector "receiving the signal"); at least if sender and detector are distinct participants, or even separated from each other. $\endgroup$ Commented Jul 16, 2014 at 5:20