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- Thread starter tickle_monste
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individual photon has no reference frame, as it has no location.

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

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JesseM

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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).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?

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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 youPhotons 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).

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.

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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

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

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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. SeeWell, I wasn't assuming there would be recoil. If there were, wouldn't that just put the velocity of the source at a value evengreaterthan c from the photon's reference frame (remember you have been endowed with magical wizard eyes for the purposes of this thought experiment).

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-kinematics.pdf

[Added] See also Library

https://www.physicsforums.com/library.php?do=view_item&itemid=19

See also post # 11 in

https://www.physicsforums.com/showthread.php?t=328050&highlight=lorentz+transform

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JesseM

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I don't understand the distinction, all statements about what would happen in an inertial coordinate system are equivalent toThis 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 youobservewill 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.

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 ofIt 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).

Inertial coordinate systems in SR areWhat 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.

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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:You're confused, the issue has nothing to do with photons not being able to catch each other--why would it?

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

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JesseM

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They don't have to adjust for the speed of light if they define coordinates of events usingFor 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?

At a theoretical level this can be derived from the two postulates of relativity, which say that 1) if different inertial observers use local measurements on these types of physical networks to define the coordinates of events, then when they write down the equations for the fundamental laws of physics in terms of their own coordinate system, they will all get the same equations; and 2) that if different inertial observers use local measurements on their own networks to measure the speed of a light beam, they will all find that it has a coordinate velocity of c. Logically you can show that the only way for these two postulates to both be satisfied is if the coordinates of different inertial observers are related by the Lorentz transform, from which you can derive length contraction and time dilation. And if you actually had a bunch of such networks moving at relativistic speeds relative to one another, you could use them totickle_monste said:You bring up clocks and measuring rods, but how do you derive the phenomena of length contraction and time dilation?