# Does time stop for a photon? Why is that a nonsensical question?

• JamieForum
In summary, the answer to this question is that photons have zero mass and always travel the speed of light. It is impossible to imagine what it would be like for a photon to be at rest, as this would lead to paradoxes.f

#### JamieForum

From this link http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html I don't understand the following..."Does time stop for a photon?. . . It is really not possible to make sense of such questions and any attempt to do so is bound to lead to paradoxes. There are no inertial reference frames in which the photon is at rest so it is hopeless to try to imagine what it would be like in one."

In particular this statement "There are no inertial reference frames in which the photon is at rest". Can anyone explain that to me?

I believe the answer to your question is that light is defined as photons, so photons are, always, traveling the the speed of light ($c$). This is why photons are said to have $0$ mass.

One of the postulates of Special Relativity is that light moves at the same speed, c, in vacuum, in all inertial reference frames. This postulate immediately says that there is no reference frame in which the light is NOT moving at c, and "at rest" is definitely not moving at c.

In SR and GR there is a well-defined mathematical procedure to calculate proper time for moving objects along trajectoreis through spacetime (as measured by a co-moving clock). Applying this procedure to a light-like trajectory (along which photons move) the result is always zero, i.e. proper time for photons vanishes. In that sense photons are 'timeless'.

In particular this statement "There are no inertial reference frames in which the photon is at rest". Can anyone explain that to me?

Although one could possibly device some frame of reference in which a photon is at rest, that frame is not a Lorentz inertial system of spacetime coordinates (called "inertial reference frame" for short).

An inertial frame is one in which the principle of relativity holds - relative to an inertial frame, moving faster but at constant speed, the laws of physics take the "same form" as when one is not moving. This is due to a symmetry in the laws of physics called "Poincare invariance".

I do not like the argument that because we cannot make a frame of reference the question is nonsensical. Frames of reference have no physical significance as they do not exist in nature.

As tom.stoer pointed out one does not need a frame of reference to demonstrate that the total elapsed time for the path of a photon between two events is zero.

I do not like the argument that because we cannot make a frame of reference the question is nonsensical. Frames of reference have no physical significance as they do not exist in nature.

As tom.stoer pointed out one does not need a frame of reference to demonstrate that the total elapsed time for the path of a photon between two events is zero.

I don't agree fully with the first statement since with special relativity, inertial frames of reference are privileged because of Poincare symmetry, which is absolute.

I do agree with the second statement as providing a good meaning to "time stops for a photon".

I don't agree fully with the first statement since with special relativity, inertial frames of reference are privileged because of Poincare symmetry, which is absolute.

I think a better way to put this might be that Lorentz boosts take timelike lines into *other* timelike lines, and spacelike lines into *other* spacelike lines, but they take null lines into themselves. So a "frame" constructed using null axes (two null and two spacelike axes for a standard set of null coordinates) will behave fundamentally differently under Lorentz boosts than an ordinary inertial frame constructed using one timelike and three spacelike axes. Since the "frame of a photon", in so far as one can construct one, would have to be constructed using null axes, it is a fundamentally different type of object than an ordinary inertial frame.

That's why saying that "time stops for a photon" is not really a good way, IMO, to convey the difference between null objects and timelike objects, since it invites the inference that a "photon frame" is just like an ordinary inertial frame, only "moving at c". Saying that the "length" of a photon's worldline is always zero between any two events on it is better, but calling that length "elapsed time" is still dodgy, IMO, because it again invites the erroneous inference. I would say that the concept of "proper time" or "elapsed time for the object" simply doesn't apply to objects that move on null worldlines. If amplification is needed, see my first paragraph above.

PeterDonis, I, of course, have no technical disagreement with what you say, only a poetic one - we shouldn't have to give up our favourite kludges, I think;)

I think a better way to put this might be that Lorentz boosts take timelike lines into *other* timelike lines, and spacelike lines into *other* spacelike lines, but they take null lines into themselves. So a "frame" constructed using null axes (two null and two spacelike axes for a standard set of null coordinates) will behave fundamentally differently under Lorentz boosts than an ordinary inertial frame constructed using one timelike and three spacelike axes. Since the "frame of a photon", in so far as one can construct one, would have to be constructed using null axes, it is a fundamentally different type of object than an ordinary inertial frame.

That's why saying that "time stops for a photon" is not really a good way, IMO, to convey the difference between null objects and timelike objects, since it invites the inference that a "photon frame" is just like an ordinary inertial frame, only "moving at c". Saying that the "length" of a photon's worldline is always zero between any two events on it is better, but calling that length "elapsed time" is still dodgy, IMO, because it again invites the erroneous inference. I would say that the concept of "proper time" or "elapsed time for the object" simply doesn't apply to objects that move on null worldlines. If amplification is needed, see my first paragraph above.
But Peter, don't you think a frame is just a mathematical object?

For instance asking "What would the rate of a clock be if we discount the light travel time of a given Doppler shift of an object which is in relative motion to us" is interesting for professors to ask students in a test but apart from that what is the scientific value of those questions, frames or planes of simultaneity do not really exist, or do you disagree?

frames or planes of simultaneity do not really exist, or do you disagree?

The planes of simultaneity certainly exist, at least to the same extent that the spacetime as a whole exists. If you adopt the viewpoint that spacetime, as a whole, is a 4-dimensional geometric object, then obviously you can "cut" particular spacelike 3-surfaces out of that 4-dimensional object that are orthogonal to particular timelike worldlines at particular events. The worldlines and the 3-surfaces themselves are coordinate-independent geometric objects, and they are as "real" as the overall geometric object that they are parts of.

Labeling the coordinate-independent geometric objects with particular coordinates is arbitrary and doesn't affect the physics. So I would agree that "frames", in the sense of particular coordinate labelings, "do not really exist". But the things that the coordinates label do (at least in the same sense that spacetime itself does).

For instance asking "What would the rate of a clock be if we discount the light travel time of a given Doppler shift of an object which is in relative motion to us" is interesting for professors to ask students in a test but apart from that what is the scientific value of those questions

If the question you quoted in the above is equivalent to the question "How much proper time elapses along this timelike worldline between events A and B?", then that question seems to me to have a direct physical meaning, since the proper time in question is directly measurable by a clock traveling along the given worldline.

Questions about "proper length" and more generally about surfaces of simultaneity are more complicated to correlate to direct physical measurements, since you first have to talk about clock synchronization and the relativity of simultaneity. But it can still be done. Whether or not it is *useful* to do it depends on the problem. Over small distances it seems to me to be useful; for example, it's hard to talk about local inertial frames and what happens in them without talking about proper length measurements within those frames. But it can be problematic when people try to extend it out over large distances, such as the recent threads about what is happening "now" on Mars or in the Andromeda galaxy. In those cases I agree that trying to assign some sort of "real meaning" to a particular surface of simultaneity causes confusion and doesn't help with understanding the physics.

If the question you quoted in the above is equivalent to the question "How much proper time elapses along this timelike worldline between events A and B?", then that question seems to me to have a direct physical meaning, since the proper time in question is directly measurable by a clock traveling along the given worldline.
No of course it is not.
But even in this case another observer can calculate the total time on the other clock by observing the Doppler shift between the events. No such planes of simultaneity are neccesary.

I think that if we stick to relativistic Doppler shift, proper distance and proper velocity (celerity) special relativity becomes a lot simpler.

No of course it is not.

Huh? Either I'm misunderstanding you or you misunderstood what I said. I said that the proper time elapsed along a given timelike worldline is directly measurable by a clock moving along that worldline. Are you disputing that? Or are you just saying that wasn't the same question you were describing with "What would the rate of a clock be if we discount the light travel time of a given Doppler shift of an object which is in relative motion to us"? If the latter, I'm not sure I understand what question you were describing.

But Peter, don't you think a frame is just a mathematical object?

Every aspect of any model is a mathematical object. If you claim you want to eliminate them and only with what there is in nature, you would have empirical evidence and exactly zero theories to explain anything. "The sun is here at this time, the sun is here at this later time and here at this later time. We do not seek to explain why."

So, your attempt to dismiss mathematical objects would stop inquisitiveness in its tracks.

"Of course it is not equivalent."
That is what I meant.

There is a difference to me between how allegedly two clocks are running with a different rate when they are in relative motion and two clocks going between two events with a different path in spacetime. The first can never be proven while the second obviously can.

Every aspect of any model is a mathematical object. If you claim you want to eliminate them and only with what there is in nature, you would have empirical evidence and exactly zero theories to explain anything. "The sun is here at this time, the sun is here at this later time and here at this later time. We do not seek to explain why."

So, your attempt to dismiss mathematical objects would stop inquisitiveness in its tracks.
I really do not think you understand what I was saying.

Every aspect of any model is a mathematical object. If you claim you want to eliminate them and only with what there is in nature, you would have empirical evidence and exactly zero theories to explain anything. "The sun is here at this time, the sun is here at this later time and here at this later time. We do not seek to explain why."

So, your attempt to dismiss mathematical objects would stop inquisitiveness in its tracks.

Surely "sun" and "here" are also mathematical models. I'm a brain in a vat:)

SR predicts that if you try to experimentally set-up a global inertial frame, you can succeed. GR predicts that you will fail. So the existence of global inertial frames is a prediction of SR (which has been falsified by GR). So inertial frames are very important in SR.

I really do not think you understand what I was saying.
I think I do. It is quite a simple concept.

You take for granted most mathematical constructs in science. This one rubs you the wrong way so you want to weaken it by claiming it doesn't exist in nature. Well, neither does relativity or spatial curvature or geodesics.

I would be interested to see you have any further meaningful discussion in this thread (let alone on PF) without resorting to some aspect of a model that does not exist in nature. Last edited:
Surely "sun" and "here" are also mathematical models. I'm a brain in a vat:) but no. Even as a brain is a vat, you can still report what your senses tell you.

You take for granted most mathematical constructs in science.
Mathematical constructs are useful if they can be used to predict experiments.

What does a plane of simultaneity predict?

"Of course it is not equivalent."
That is what I meant.

There is a difference to me between how allegedly two clocks are running with a different rate when they are in relative motion and two clocks going between two events with a different path in spacetime. The first can never be proven while the second obviously can.

Ah, ok. So your question was describing #1 and mine was describing #2. I agree that #2 is a direct observable but #1 is not.

Ah, ok. So your question was describing #1 and mine was describing #2. I agree that #2 is a direct observable but #1 is not.
Yes, and in my opinion educators spend an undeserved disproportionate amount of time on #1 issues.

Indeed matters such as 'seeing different times (or whatever grandiose ways of describing it)' on Earth for observers on Andromeda walking a stroller versus standing still are rather useless compared to doing a calculation with for instance Doppler shifts.

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I don't think #2 is a "direct observable". It requires an ideal clock. But an ideal clock is defined as one that measures elapsed proper time. So before you observe it, you have to make sure you have an ideal clock. How do you make sure you have such a clock?

I don't think #2 is a "direct observable". It requires an ideal clock. But an ideal clock is defined as one that measures elapsed proper time. So before you observe it, you have to make sure you have an ideal clock. How do you make sure you have such a clock?
There several experiments done with clocks aboard planes that clearly show the effects of time dilation.

There several experiments done with clocks aboard planes that clearly show the effects of time dilation.

Did they calibrate the clocks without setting up inertial frames?

I don't think #2 is a "direct observable". It requires an ideal clock. But an ideal clock is defined as one that measures elapsed proper time. So before you observe it, you have to make sure you have an ideal clock. How do you make sure you have such a clock?

Any "twin paradox" scenario clearly shows that the elapsed proper time between two given events depends on the path taken, i.e., the specific worldline followed. The Hafele-Keating type experiments that Passionflower mentions are examples of such scenarios, though they do require GR to accurately predict the results so they're not as simple as the standard twin paradox scenario. Those experiments also establish that we can build actual physical clocks whose readings correspond very closely to the calculated readings for the worldlines they follow. If all this doesn't meet your definition of "direct observable", then at that point I think the issue is one of language, not physics.

Any "twin paradox" scenario clearly shows that the elapsed proper time between two given events depends on the path taken, i.e., the specific worldline followed. The Hafele-Keating type experiments that Passionflower mentions are examples of such scenarios, though they do require GR to accurately predict the results so they're not as simple as the standard twin paradox scenario. Those experiments also establish that we can build actual physical clocks whose readings correspond very closely to the calculated readings for the worldlines they follow. If all this doesn't meet your definition of "direct observable", then at that point I think the issue is one of language, not physics.

Can't I build a "clock" that travels on a null geodesic and returns a null reading? Say the clock is two beams of light of different frequencies. The "elapsed time" is the change in phase between them from the initial phase.

Jamie, it's a tricky question. If I can measure a photon that I know has been sent out by a source like some laser, and finds that to take a 'time' according to my clock, can that photon at the same time be 'time less'? We do have a propagation for it, 'c'.

And somehow 'photons propagates' inside our measure of time. On the other hand, if now 'photons' isn't 'time less', how can they still be existing there in the Cosmic Microwave Background radiation? That is approximately 13.7 billion years ago as we understands it today.

Most of the astrophysics would have to be redefined if it was wrong, as I think. And the models we have make good sense even though there isn't a 'theory of everything' so far.

How Old is the Universe?

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Did they calibrate the clocks without setting up inertial frames?
What is the difficulty?

If we have an experiment where two clocks go between two events using different paths in spacetime then both at the start and end event they are obviously co-located. So at the start we just make sure they show the same time and at the end we check their times again.

No frames or planes of simultaneity are necessary.

Mathematical constructs are useful if they can be used to predict experiments.

What does a plane of simultaneity predict?

The "initial value problem" often has data specified on a plane of simultaneity.

For example, given the electromagnetic field at a "given time" [i.e. on a plane of simultaneity], use maxwell's equations to determine the electromagnetic field at events in the future.

Another example is the wave equation
http://en.wikipedia.org/wiki/Wave_equation

Jamie, it's a tricky question. If I can measure a photon that I know has been sent out by a source like some laser, and finds that to take a 'time' according to my clock, can that photon at the same time be 'time less'? We do have a propagation for it, 'c'.

And somehow 'photons propagates' inside our measure of time. On the other hand, if now 'photons' isn't 'time less', how can they still be existing there in the Cosmic Background radiation? That is approximately 13.7 billion years ago as we understands it today.

Most of the astrophysics would have to be redefined if it was wrong, as I think. And the models we have make good sense even though there isn't a 'theory of everything' so far.
Actually there are two ways of thinking about time dilation:

If we take a situation where we have two clocks going between events A and B on different spacetime paths we could say that :

"One clock ran slower than the other".

but we could also say that:

"Both clocks run at the same rate however, one clock took a path in spacetime that took simply less time as, by analogy, some roads from city A to B take less miles".

We cannot prove one is more valid than the other, however my personal preference is for the latter explanation.

In the interpretation of the latter explanation we can say that it is actually not true that time freezes for photons, time goes the same for everything in the universe including photons however, the paths that photons take in spacetime simply take no time whatsoever.

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What is the difficulty?

If we have an experiment where two clocks go between two events using different paths in spacetime then both at the start and end event they are obviously co-located. So at the start we just make sure they show the same time and at the end we check their times again.

No frames or planes of simultaneity are necessary.

OK, let's say you did the experiment and the SR prediction is not verified. Were the clocks broken or is SR wrong?

OK, let's say you did the experiment and the SR prediction is not verified. Were the clocks broken or is SR wrong?
Well that would be a problem.

But guess what?
We are lucky, as the experiments confirm SR!