# Another 'photon's reference frame' thread

If we can shoot a photon outward, at velocity c, why is it that the body that shot it outward is not traveling away from the photon with velocity c?

individual photon has no reference frame, as it has no location.

individual photon has no reference frame, as it has no location.
So how is it that we say that it travels with any speed at all, and if it's traveling away from its source of emission, why is that source not traveling away from it with velocity c?

JesseM
So how is it that we say that it travels with any speed at all, and if it's traveling away from its source of emission, why is that source not traveling away from it with velocity c?
Photons do have a location in any given inertial frame, but they don't have an inertial rest frame of their own. In any given inertial frame, if you take the photon's position coordinate at one time coordinate and then look at the same photon's position coordinate at a different time coordinate, you will have (change in position)/(change in time) = c (as long as it was traveling in a vacuum the whole time).

Photons do have a location in any given inertial frame, but they don't have an inertial rest frame of their own. In any given inertial frame, if you take the photon's position coordinate at one time coordinate and then look at the same photon's position coordinate at a different time coordinate, you will have (change in position)/(change in time) = c (as long as it was traveling in a vacuum the whole time).
This is all very much the domain of special relativity, which is nothing more than a matter of observation. Basically, if you're moving in some manner: accelerating, uniform, w/e, photons will catch up to you differently, and what you observe will differ between different frames of reference. This is all that the Lorentz transformations describe, so when you try to consider a body that photons can't catch up to, i.e. another photon, it's no wonder the theory breaks down, and actually speaks to it's accuracy (incomplete, though it may be). But that's just it, special relativity describes only what is observed, not what is reality. It is for different reasons from general relativity that a particle with mass cannot be accelerated to the c, but that's always the first reason attempts to imagine a photons reference frame are shot down. But now I'm going to just start out assuming that particle is massless, just like the photon who's reference frame I'm trying to understand, so I have absolutely no problem sending this particle right alongside the photon. Now, the second reason all attempts are shot down is because of the notion, derived from special relativity, that the photon should have no reference frame. So, again, this is ONLY, (only? yes, only) because photons can't catch up to one another. Did I say that that's the ONLY reason for the breakdown of the theory at the speed of light? Cause if I didn't: that's the ONLY reason (in special relativity).

By analogy, let's say particles with mass are aircraft carriers, and they always travel at less than 60mph. Nothing in this thought experiment emits light; light is not a factor in this thought experiment. The aircraft carriers decide what to do based on messages received from little speed-boats that travel between aircraft carriers at a constant velocity of 60mph. Nobody in the entire experiment has any information to go by except that which was obtained through the messages delivered by the speed-boats. So if aircraft carriers A and B are sending messages to each other via speedboat, and are stationary relative to one another, then it will take a certain amount of time for an aircraft carrier to be "illuminated" by a message. If A is stationary, and B is moving away from A at 5mph, then it will take a longer amount of time for B to be illuminated by messages received from A. If B constructs for itself a coordinate system that is based solely off the manner in which these messages are received, then the theory of special relativity would apply just as well to speed-boats and aircraft carriers as it does photons and particles, and it would break down in exactly the same way when we try to imagine one of the aircraft carriers traveling at 60 mph, or the reference frame of a speed boat. The speed boats can't go faster than 60 mph, so if something else were traveling at 60 mph, the speed boat wouldn't catch up, and wouldn't transmit information, and any theory based on the transmission of information would break down in this scenario.

Luckily, we have eyes, and photo-receptor plates, so we don't have to rely on 60mph information, we can rely on 2.9979x10^8m/s information, using our eyes. But these photons are just like faster speed boats, and particles like the aircraft carriers, and once again, ANY theory of observation that's based off the transmission of information at a finite speed will break down when you try to consider other objects traveling at that speed. But these are NOT absolute limitations to imagining it. In fact, we can get around just about EVERY limitation 'imposed' upon our imagination by special relativity: let's just assume we have magical wizard eyes that, at every moment, can perceive EVERYTHING that is happening simultaneously (actual simultaneity, not things appearing to be simultaneous). I mean, that's almost what we're trying to accomplish with the whole theory of relativity anyway: our eyes don't reveal exactly what's happening, so we have to adjust based on physical principles.

What I'm getting at is that it's not, in any way, nonsensical to attach a coordinate frame to a photon. The only thing that's nonsensical is to try to attach a coordinate frame that is constructed by what the photon 'observes' via the intake of other photons; the whole thing is just undefined.

A photon is emitted at time t=0. At time t=t'>0, there is a distance d=ct' separating the photon and its source. So I ask the question, how fast is the source traveling?

v=d/t.
d=ct'
t=t'.
v=ct'/t'=c.
The source is traveling at the speed of light relative to the photon.

If a nuclear isomer emits a gamma ray and recoils, the momentum of the emitted photon and of the recoil nucleus are equal. Because the nuclear mass is so high, the recoil is in most cases negligible.

If a nuclear isomer emits a gamma ray and recoils, the momentum of the emitted photon and of the recoil nucleus are equal. Because the nuclear mass is so high, the recoil is in most cases negligible.
Well, I wasn't assuming there would be recoil. If there were, wouldn't that just put the velocity of the source at a value even greater than c from the photon's reference frame (remember you have been endowed with magical wizard eyes for the purposes of this thought experiment).

individual photon has no reference frame, as it has no location.
In a transparent medium the light velocity is smaller than "c" so there is a co-moving reference frame where the light is at rest and the emitter moves at v<c.

Well, I wasn't assuming there would be recoil. If there were, wouldn't that just put the velocity of the source at a value even greater than c from the photon's reference frame (remember you have been endowed with magical wizard eyes for the purposes of this thought experiment).
How about the annihilation of the positron with an electron at rest. After the positron has annilated with the emission of one 511 KeV photon traveling away at the velocit of light, all that is left is another 511 KeV photon traveling in the opposite direction, also at the velocity of light. This should all be covered in the Lorenttz transformation. See
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-kinematics.pdf
https://www.physicsforums.com/library.php?do=view_item&itemid=19

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JesseM
This is all very much the domain of special relativity, which is nothing more than a matter of observation. Basically, if you're moving in some manner: accelerating, uniform, w/e, photons will catch up to you differently, and what you observe will differ between different frames of reference. This is all that the Lorentz transformations describe, so when you try to consider a body that photons can't catch up to, i.e. another photon, it's no wonder the theory breaks down, and actually speaks to it's accuracy (incomplete, though it may be). But that's just it, special relativity describes only what is observed, not what is reality.
I don't understand the distinction, all statements about what would happen in an inertial coordinate system are equivalent to physical statement about which events would happen next to which ruler-markings, and what readings the clocks at those ruler-markings are showing when the events happen in their vicinity, on a physical network of inertial rulers and clocks constructed according to Einstein's procedure for defining inertial coordinate systems. If a photon was next to the 10-light-second mark on a ruler when the clock there read 30 seconds, then if the same photon was later next to the 20-light-second mark on the same ruler, it would be true that the clock at that mark read 40 seconds as the photon was passing it. Are these not statements about physical "reality"? Of course you are free to construct a non-inertial coordinate system in which a photon is moving at some other speed besides c, SR does not forbid this, it just says that the equations for the laws of physics will look different when you express them in this coordinate system then they do in inertial coordinate systems (where they will look the same regardless of which inertial coordinate system you choose).
It is for different reasons from general relativity that a particle with mass cannot be accelerated to the c, but that's always the first reason attempts to imagine a photons reference frame are shot down. But now I'm going to just start out assuming that particle is massless, just like the photon who's reference frame I'm trying to understand, so I have absolutely no problem sending this particle right alongside the photon. Now, the second reason all attempts are shot down is because of the notion, derived from special relativity, that the photon should have no reference frame. So, again, this is ONLY, (only? yes, only) because photons can't catch up to one another. Did I say that that's the ONLY reason for the breakdown of the theory at the speed of light? Cause if I didn't: that's the ONLY reason (in special relativity).
You're confused, the issue has nothing to do with photons not being able to catch each other--why would it? You are free to construct a coordinate system where a photon is at rest, it just won't be an inertial one, so the equations of SR that work in inertial frames (the time dilation equation) wouldn't apply here. And in fact, you could construct an infinite number of different coordinate systems where a photon was at rest, which would disagree about things like the times and distances between various events (unlike in the case with inertial frames, where there is a single answer to these types of questions if you want to use a given object's inertial rest frame); there's no physical basis to treat any of these coordinate systems as better representing a photon's "perspective" then any other, because the times and distances are not based on actual rulers and clocks which are at rest relative to the photon, they're just chosen arbitrarily (you can't actually have rulers and clocks moving at the speed of light, and even if you consider the limit as they approach the speed of light, the clocks would approach being frozen and the rulers would approach being shrunk to zero length, so these limiting cases don't make a sensible basis for constructing a coordinate system).
What I'm getting at is that it's not, in any way, nonsensical to attach a coordinate frame to a photon. The only thing that's nonsensical is to try to attach a coordinate frame that is constructed by what the photon 'observes' via the intake of other photons; the whole thing is just undefined.
Inertial coordinate systems in SR are not usually imagined as being constructed based on what any observer sees using light signals; rather, they are imagined as being constructed based on local readings on a network of inertial rulers and clocks which fill space (so every event happens right next to some ruler-marking and clock-reading in the network) and which are at rest relative to the observer. The only place light plays a role is in defining what it means for clocks at different locations to be "synchronized" in a given frame (the idea is that if you set off a flash at the midpoint of two inertial clocks, and both clocks show the same time at the moment the light from the flash reaches them, then the clocks are defined to be synchronized in their own rest frame, although other frames will say they are out-of-sync due to the relativity of simultaneity). But even this is not strictly necessary, an equivalent synchronization procedure is to synchronize two clocks when they are right next to each other (and at the midpoint of the locations you want to move them to), then move them apart very slowly at equal and opposite velocities in the frame you want to use them in.

You're confused, the issue has nothing to do with photons not being able to catch each other--why would it?
For the most part, we're saying the same thing in different languages, but it does have something to do with photons not being able to catch each other. Enter lightning bolt:

Lightning strikes at time t=0 at location x=0. A person is standing at location x=1. When will they say the lightning bolt occurs, before they've adjusted for the speed of light? They'll say it occurs when the light from the lightning bolt reaches their eyes, at time t=t', whenever that is (it's given). Now, they can obtain a more accurate estimate for when the lightning strike occurred by adjusting for the speed of light:
d=ct. d=1, t=t'. 1=ct'; t'=1/c. t'-(1/c)=0, so they would conclude that the lightning bolt ACTUALLY struck at time t=0, but it didn't register until time t=t'. The greater x is, the greater t' will be, because it takes longer for photons to reach you. The Lorentz transformations are just this, but generalized to apply to a changing x. In other words, all the Lorentz transformations tell you is how long it takes different photons to reach you, depending on the manner in which you're changing your state of motion. Traveling at the speed of light, photons can't reach you. The theory HAS to break down at this limit, because the whole thing is physically meaningless if photons can't catch each other (which they can't), and that's exactly what it does (which speaks to the accuracy of the theory). It doesn't just have something to do with photons not being able to catch each other, it ONLY has to do with photons being able to catch each other. You bring up clocks and measuring rods, but how do you derive the phenomena of length contraction and time dilation? With the idea that depending on the state of motion of your measuring rod or your clock, you will observe different things due to the finite speed of light. EVERYTHING from special relativity goes back to how long it takes photons to reach things

JesseM