# Does a photon have a frame of reference?

## Main Question or Discussion Point

My thinking has been that a photon, in its own F of R, in a vacuum, travels through space, but not through time. This seems to have been "confirmed" in various things I have read.

However, I recently came across the assertion that "...in physics, there is no theory that defines the frame of reference of a photon". The conclusion drawn from this was that it cannot be reasoned that a photon does not experience time. Is this right?

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Drakkith
Staff Emeritus
Where did you come across this assertion?

rcgldr
Homework Helper
The math for sub-light speed objects shows that as those objects approach light speed, time slows down and the limit at light speed would have time stopped. However that mathematical model shouldn't be applied to photons that only exist a light speed.

Photons can't "observe" anything, but they do have frequencies, and those frequencies could be considered to be the photons clocks, which could mean that time isn't stopped for photons. The number of cycles between emission and absortion of a photon could be considered the number of clock ticks during the photon's "life span".

Using an analogy to equivalence theory, the observation of a beam of light from some sub-light speed object should not be significantly different than the observation of that sub-light speed object from the beam of light (if it were possible for photons to "observe").

Rap
The math for sub-light speed objects shows that as those objects approach light speed, time slows down and the limit at light speed would have time stopped. However that mathematical model shouldn't be applied to photons that only exist a light speed.
This is not correct. Time does not slow down for a "moving" object. There is no such thing as a "moving" object, only objects which move with respect to some other object. If A and B are observers moving with respect to each other, then a clock moving with A will tick "normally" according to A, but slowly according to B. A clock moving with B will tick "normally" according to B, but slowly according to A.

Photons can't "observe" anything, but they do have frequencies, and those frequencies could be considered to be the photons clocks, which could mean that time isn't stopped for photons. The number of cycles between emission and absortion of a photon could be considered the number of clock ticks during the photon's "life span".
This is not correct. Different observers will assign different frequencies to the photon. If A observes a photon as having a certain frequency, and B is moving in the same direction as the photon (according to A) then B will observe a lower frequency for that photon (i.e. a "red shift). As the speed of B with respect to A approaches that of light, the frequency of the photon will approach zero.

You can get a feel for how things work by considering speeds close to the speed of light. Lets say A and B are moving at a*c with respect to each other, where c is the speed of light. Lets say a=1-5e-28, a number VERY close to one, which gives a gamma of about 32 trillion. Lets say that each has a clock that ticks off seconds, and both clocks tick just as they pass each other. A will have to wait 32 trillion seconds (about a million years) for B's next tick, and B will have to wait a million years for A's next tick. If A were on the earth, B would observe A and its environment as nearly frozen in time. According to B it would take 32 trillion years for the earth to orbit the sun once. The mass of the earth would be 32 trillion times the mass that A measures earth's mass to be. If B were on a planet like earth, orbiting its sun once a year, then according to A it would take 32 trillion years for B's planet to orbit its sun once, and its earth-like planet would have 32 trillion times the mass of the earth. Now take the leap - suppose B were a photon, travelling at light speed. It would experience time normally, but it would see the universe as absolutely frozen in time, with all massive objects (like A) moving at light speed, with infinite mass. Impossible.

Using an analogy to equivalence theory, the observation of a beam of light from some sub-light speed object should not be significantly different than the observation of that sub-light speed object from the beam of light (if it were possible for photons to "observe").
Such equivalence can never exist. Any sub-light speed object must have rest mass greater than zero, any light-speed object must have zero rest mass. So to speak.

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rcgldr
Homework Helper
I recall reading some article that the rules for sub-light speed objects regarding space and time don't apply to photons, but can't find a link, and I don't recall the details. Sub-light speed observers can see that photons have a frequency, that the speed of light isn't infinite, that light is affected by gravity fields, ... but these are effects that the photon itself could not observe.

Perhaps it's simpler to state that a light speed frame of reference doesn't fit with the normal concept of a frame of reference.

I'm confused, don't worry, happens all the time here...

Is it true that a photon emitted 13 LY away could be absorbed by a telescope on Earth with the photon "thinking" that no time elapsed, that it's time of travel was zero?

Now, suppose I invent a way to become massless, and to also make my wristwatch massless. and I invent a way to latch onto that photon, hitch a ride on it.

Here's my problem: In the Alice and Bob SR puzzles, Alice's clock ticks normally despite the fact that she is traveling like 0.9999c. Seems like my wristwatch therefore ought to keep ticking normally as I ride the photon, my time is "normal" within my frame of reference.

But the photon gets there instantly, and by my watch, it takes 13 billion years. Something is definitely wrong here. Someone please unscrew my brain about this...

Thanks, OF

JesseM
I'm confused, don't worry, happens all the time here...

Is it true that a photon emitted 13 LY away could be absorbed by a telescope on Earth with the photon "thinking" that no time elapsed, that it's time of travel was zero?

Now, suppose I invent a way to become massless, and to also make my wristwatch massless. and I invent a way to latch onto that photon, hitch a ride on it.

Here's my problem: In the Alice and Bob SR puzzles, Alice's clock ticks normally despite the fact that she is traveling like 0.9999c. Seems like my wristwatch therefore ought to keep ticking normally as I ride the photon, my time is "normal" within my frame of reference.

But the photon gets there instantly, and by my watch, it takes 13 billion years. Something is definitely wrong here. Someone please unscrew my brain about this...

Thanks, OF
See [post=2692028]this post[/post]--basically my answer would be that a photon doesn't have an inertial frame of its own so the usual statements about how things work in inertial frames (like 'my wristwatch therefore ought to keep ticking normally ... my time is "normal" within my frame of reference') don't apply, but you can think about what would be true in the limit as your speed relative to the galaxy approached c, and in this limit the distance in your frame between opposite ends of the galaxy would approach zero in your frame due to length contraction, which explains why even in your frame the time on your clock to get from one end to the other approaches zero as well.

In such a limit, the traveler will see all the clocks at rest relative to the galaxy (or close to it) as approaching zero rate of ticking, and also sees the length of the galaxy in the direction of motion as squashed down to near zero.
This is the perspective I have come to myself as making the most sense...I mean to me....time dilation and length contraction are related phenomena as the speed of light is approached. Netiher makes "ordinary" sense, but when thought of together the real dichomety from everyday slow speed experience provides some perspective.

I have never quite figured to my own satisfaction out why a photon doesn't actually have it own inertial frame, but when I think neither time nor distance have much meaning at v = c, I can better relate to that circumstance....and from that deduce defining an inertial frame without time nor distance would be really awkward.

JesseM
I have never quite figured to my own satisfaction out why a photon doesn't actually have it own inertial frame, but when I think neither time nor distance have much meaning at v = c, I can better relate to that circumstance....and from that deduce defining an inertial frame without time nor distance would be really awkward.
Well, you can certainly construct a coordinate system where a photon is at rest, but the basic reason it doesn't qualify as "inertial" is that calling it that would mean the two postulates of relativity don't work in all inertial frames (you can still have perfectly good non-inertial coordinate systems where a photon is at rest, but there are multiple possible ways of building such a coordinate system so there's no reason to pick out any one and say it represents the 'perspective' of a photon). Also, inertial frames are defined physically in terms of clocks and rulers at rest in the frame, but of course we can't accelerate a clock or ruler to the speed of light.

My thinking has been that a photon, in its own F of R, in a vacuum, travels through space, but not through time. This seems to have been "confirmed" in various things I have read.

However, I recently came across the assertion that "...in physics, there is no theory that defines the frame of reference of a photon". The conclusion drawn from this was that it cannot be reasoned that a photon does not experience time. Is this right?
Nearly so, and quite. No material thing can go as fast as light. In that unattainable limit, any "F of R" would be at the speed of light 0 m long and any of its clocks would be completely stopped; our definition of F of R doesn't apply to that. Einstein formulated it as follows in his famous paper:

"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."

D H
Staff Emeritus
In that unattainable limit, any "F of R" would be at the speed of light 0 m long and any of its clocks would be completely stopped; our definition of F of R doesn't apply to that.
Just to elaborate, let's look at a perfectly coherent beam of light (no divergence as in a real laser beam). This is a perfectly coherent beam: An inertial observer would see all photons in the beam as traveling in exactly the same direction.

Problem #1: In the frame of reference of some photon in that beam, what is the velocity of some other photon in the beam? We have a slight problem here with the second postulate of special relativity, which says that the local speed of light is the exact same value, c, in all reference frames.

Problem #2: Another aspect of special relativity is that one can transform from any one inertial frame to another using the Poincare transform. Try going to/from the photon frame of reference using this transformation. There will be a slight problem with dividing by zero / multiplying by infinity here.

In short, the concept of a photon's frame of reference is ill-defined. It doesn't make any sense.

Fredrik
Staff Emeritus
Gold Member
However, I recently came across the assertion that "...in physics, there is no theory that defines the frame of reference of a photon". The conclusion drawn from this was that it cannot be reasoned that a photon does not experience time. Is this right?
The reference frame of a particle moving at 299792458 m/s without ever accelerating is well-defined in pre-relativistic classical mechanics. So it's not right to say that there's no theory that defines it. It just isn't defined in any theory that's better than special relativity. It's ill-defined in both SR and GR.

If you would like to know more about why it's ill-defined in SR, I suggest you check out my posts in this thread.

Rap
Is it true that a photon emitted 13 LY away could be absorbed by a telescope on Earth with the photon "thinking" that no time elapsed, that it's time of travel was zero?
Yes, in the sense that if a massive particle was emitted 13 LY away travelling at very near the speed of light, it would reach the earth in a very short time, maybe a minute, according to its own clock.

Now, suppose I invent a way to become massless, and to also make my wristwatch massless. and I invent a way to latch onto that photon, hitch a ride on it.

Here's my problem: In the Alice and Bob SR puzzles, Alice's clock ticks normally despite the fact that she is traveling like 0.9999c. Seems like my wristwatch therefore ought to keep ticking normally as I ride the photon, my time is "normal" within my frame of reference.

But the photon gets there instantly, and by my watch, it takes 13 billion years. Something is definitely wrong here. Someone please unscrew my brain about this...
No, by your watch it will get there instantaneously. Its better to talk about things very near the speed of light, rather than at the speed of light, its easier to understand things. If you were riding along on a particle that was very near the speed of light with respect to earth and it was 13 LY away by earth measurement when you started your watch, your watch would measure only a very small amount of time to get to earth, maybe a minute. The earth would seem to come towards you at nearly the speed of light, but because of the Lorentz contraction, it would not be 13 LY away, but only a light minute away. Suppose the people on earth started their watch at the same time they see you starting yours. The earth people will say it takes about 13 years for you to arrive. Remember that according to you, the people on earth did not start their watch at the same time as you did (simultaneity is not absolute). To you, they started their watch long before you did. When you pass earth, your watch measures 1 minute, theirs measures about 13 years.
Extending this to a photon, you might say that by your watch, you and the photon will get there instantly, because there is no distance to travel.

HallsofIvy
Homework Helper
I'm confused, don't worry, happens all the time here...

Is it true that a photon emitted 13 LY away could be absorbed by a telescope on Earth with the photon "thinking" that no time elapsed, that it's time of travel was zero?
I think I will get my self a nice single-malt Scotch, then sit here and contemplate a photon "thinking"!

Now, suppose I invent a way to become massless, and to also make my wristwatch massless. and I invent a way to latch onto that photon, hitch a ride on it.
To even "suppose" such a thing "supposes" that special relativity is wrong. Essentially you are asking "If relativity is wrong, what would relativity say about this situation?" Perhaps if I drink enough Scotch, that question wll make sense!

[aupote]Here's my problem: In the Alice and Bob SR puzzles, Alice's clock ticks normally despite the fact that she is traveling like 0.9999c. Seems like my wristwatch therefore ought to keep ticking normally as I ride the photon, my time is "normal" within my frame of reference.

But the photon gets there instantly, and by my watch, it takes 13 billion years. Something is definitely wrong here. Someone please unscrew my brain about this...[/quote]
What is "definely wrong" is that you are setting up a situation which relativity says is impossible and then trying to apply relativity to it. You can't "have your cake and deny itls existence too".

Thanks, OF

Drakkith said:
Where did you come across this assertion?
It was in a thread on the Naked Science Forum, by a poster who usually seems to make good sense.

harrylin said:
we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.
How do you define "infinitely great velocity"?

JesseM
It was in a thread on the Naked Science Forum, by a poster who usually seems to make good sense.
The poster was correct, as various posters on this thread have noted there can be no inertial frame where a photon is at rest.
Endervhar said:
How do you define "infinitely great velocity"?
I think the quote was saying that the speed of light in relativity plays a similar role to an infinite velocity in Newtonian physics (for example, in both cases no finite acceleration will ever allow you to reach that velocity in finite time). An infinite velocity in Newtonian physics is just what it sounds like, moving at infinity meter/second, so it takes zero time to cross from one location to another.

Who asked this silly question in the first place? I did?!! Oh, well, I'm neither a scientist, nor a philosopher, so I have an excuse.

After reading the posts in this thread a few times, and following JesseM's link, I find that another silly question comes to mind: How many ways are there in which a physicist can say "I don't know?". However, I'm not going to ask that question, because I suspect that the answer could involve infinity, which in guaranteed to make things worse.

Thanks for the fascinating input, though. I look forward to more in the future.

D H
Staff Emeritus