# The Photon's Perspective Taboo

## Main Question or Discussion Point

The "Photon's Perspective" Taboo

There seems to be a general consensus that any attempt to try and imagine the universe form the reference frame of a photon is completely off limits. I don't quite understand this when taken within the context of other ideas which are presented here.

Just about every day, a thread will pop up on this forum where someone dreams up an elaborate and convoluted scenario designed to test the logical limits of relativity.

What if there is an elephant traveling a .99c, and there is a kangaroo mouse made entirely of dark matter running on his back at a counterclockwise radial velocity of .99c?

You know the drill. No matter how crazy these thought experiments get, someone will inevitably come in here and break it down piece-by-piece and figure it out. The person posing the question often doesn't even understand relativity at a basic level, yet the scenario is usually indulged and "solved" in great mathematical detail.

However, if at any point someone suggests looking at the universe from the perspective of the photon, the discussion is instantly over.

Now, before you start educating me on the myriad reasons why nothing will ever travel at the speed of light, don't worry. I know. It's impossible. That's not what this is about.

Photons exist, right? They have no mass, obviously, but they are real things which interact with the real world. Sure, they have a particle/wave duality nature, but on some level there is in effect a particle (virtual it may be) that travels from point A to point B in a given time. However, it is absolutely forbidden to even think about how this particle experiences our universe.

Isn't the very theory of relativity itself predicated upon this line of reasoning? Didn't Einstein imagine himself as an electrical impulse traveling down an electric fence in order to refine his ideas into a workable theory? Apparently, he got something useful out of it.

Why is it off-limits for discussion now? Is it because the universe becomes infinitely contracted? Is it because you have to divide by zero? We can talk about black holes all day long, and no one complains about the singularity, which requires the same thing.

I can see why someone new to relativity would be discouraged from thinking about this, because they don't fully understand how everything fits together. Once you get past the phase of trying to trick relativity with convoluted scenarios and thought experiments and accept the principles for what they are - an accurate description of reality - where is the harm in considering all possible perspectives? Just because we don't like the result doesn't mean we can't learn something from it.

I'm not trying to stir up trouble and rail against the establishment or anything. I'm just genuinely curious about this, and I think it would make an interesting discussion.

## Answers and Replies

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atyy

There is something called "light cone coordinates". However, the reference frame defined by these coordinates do not form an inertial reference frame, which is the sort of reference frame in which the "standard formulas" hold.

There is something called "light cone coordinates". However, the reference frame defined by these coordinates do not form an inertial reference frame, which is the sort of reference frame in which the "standard formulas" hold.
Exactly. Once you attempt to take on this reference frame, the standard formulas break down.

So what? How do they break down? Why do they break down? What is the underlying mechanism that makes c so special? We can still gain insight by understanding how and why certain things don't work. We can still talk about the nature of things without the formulas to describe them. How else could we have derived the standard formulas in the first place?

atyy

Exactly. Once you attempt to take on this reference frame, the standard formulas break down.

So what? How do they break down? Why do they break down? What is the underlying mechanism that makes c so special? We can still gain insight by understanding how and why certain things don't work. We can still talk about the nature of things without the formulas to describe them. How else could we have derived the standard formulas in the first place?
Yes.

atyy

Take a look at Fig 1 of http://arxiv.org/abs/hep-ph/9705477. The "instant form" uses inertial coordinates.

"In principle, all three forms should yield the same physical results, since physics should not depend on how one parametrizes the space (and the time). If it depends on it, one has made a mistake. But usually one adjusts parametrization to the nature of the physical problem to simplify the amount of practical work."

This http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html" [Broken] does a good job at explaining the "photon's perspective" by analogy. Hope this helps.

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Being new to this this discussion I hope this person typing shall sound humble. Photons are because we can not see or imagine anything more. As for relativity, I personally have no understanding of it.

There is a web of reality that we do not understand. All things are tied together in some fashion. Photons, as we call them, are nothing more than the extension of light. No mathematics about it, they are physical.

In my view, there is no light and no matter. It is a barrier we must cross. Co-existence is the key to science today. Light is subject to physical rules. Matter is the only thing we can observe.

It is my contention that neither of them truly matter in the grand scheme of things. We only think they do because we are subject to them.

Gravity is a force. A force does not obey the present laws of matter. This includes the weak, the strong. magnetism and gravity.

What I know is that matter coagulates to form something more. Why is this?

I know this does not answer your question. Presents more maybe. Being a new person the discussion of physics and our inevitable demise leaves me reeling in the sand of ignorance. Thank god for spell check.

Fredrik
Staff Emeritus
Gold Member

To understand this, you need to know what "the particle's point of view" refers to when the particle is massive (and therefore moving at speeds less than c).

Given a timelike curve (which represents the motion of a particle moving at speeds <c), there's a natural way to associate a coordinate system with it. We take the curve itself to be the time axis. The x coordinate is defined to be 0 at every point on it. Then we choose a point (any point) on the time axis and define its t coordinate to be 0. For every other point on the time axis, we define the sign of its time coordinate to be positive if it's in the future of the origin and negative if it's in the past of the origin, and we define the magnitude of its time coordinate to be the proper time from the origin to the point we're considering. (Proper time is a property of a curve, defined as the integral of $\sqrt{-g(v,v)}$ along the curve, where g is the metric and v is the tangent vector to the curve. In inertial coordinates in 1+1 dimensions, that square root simplifies to $\sqrt{dt^2-dx^2}$).

Then we assign coordinates to as many other points as possible by using a synchronization convention. The standard one says that if we emit light at (-T,0) (that's t=-T and x=0), and receive it at (T,0) after a single reflection, the reflection event has coordinates (0,cT). Note that we have defined the reflection event to be simultaneous with the event half way between emission and detection.

Note that this synchronization convention doesn't work for photons. That's why we say that "the photon's point of view" doesn't make sense. The standard definition of "a particle's point of view doesn't work". You can of course choose to define a photon's "point of view", but then the question is, why would you want to call what you just defined a "point of view" (or "perspective" or whatever)?. It's not the same thing as what you've been calling a point of view so far, so why would we want to use terminology that suggests that it is the same thing?

1. Are we considered to be absolutely stationary relative to the photons?
2. Do photons move at speed c whether towards, away from, or even passed us at any angle at all times?
3. Just on the last bit of question 2, when they travel at an angle is their speed measured as their speed at the angle or as their distance from us over time?
4. If it is their speed at the angle, then does this mean that light can change its relative distance from us at less than the speed of light?
Does that make sense or would a picture be better?

Doc Al
Mentor

1. Are we considered to be absolutely stationary relative to the photons?

2. Do photons move at speed c whether towards, away from, or even passed us at any angle at all times?
Yes.
3. Just on the last bit of question 2, when they travel at an angle is their speed measured as their speed at the angle or as their distance from us over time?
We measure their speed as the distance they travel per unit time in our frame, not as their distance from us per unit time.
4. If it is their speed at the angle, then does this mean that light can change its relative distance from us at less than the speed of light?
Sure.

Thanks for the answers Doc.
Just with the first question, if photons (in vacuum) always move at speed c relative to us than does that mean that we are considered to not me moving while the photon does all the moving?
I mean we're not considered to be moving at the speed of light relative to photons are we?

If a car moves away from us we can also be considered as moving away from the car.
But we shouldn't think of photons that way, correct?

Fredrik
Staff Emeritus
Gold Member

Just with the first question, if photons (in vacuum) always move at speed c relative to us than does that mean that we are considered to not me moving while the photon does all the moving?
You seem to think that "moving" is an objective property of a physical system. It's not. If something is described as "moving" or not depends on what coordinate system is being used.

You included the words "relative to us" in your question. That's an instruction that means that we're supposed to answer using a coordinate system in which we're not moving. So you asked if we're not moving in the coordinate system in which we're not moving.

I mean we're not considered to be moving at the speed of light relative to photons are we?
Our speed relative to a photon depends on what coordinate system you choose to call the "photon's point of view".

If a car moves away from us we can also be considered as moving away from the car.
But we shouldn't think of photons that way, correct?
You could, but it's not very useful. It's much easier to stick with inertial frames, and photons move at speed c in all inertial frames.

Note that this synchronization convention doesn't work for photons. That's why we say that "the photon's point of view" doesn't make sense. The standard definition of "a particle's point of view doesn't work". You can of course choose to define a photon's "point of view", but then the question is, why would you want to call what you just defined a "point of view" (or "perspective" or whatever)?. It's not the same thing as what you've been calling a point of view so far, so why would we want to use terminology that suggests that it is the same thing?
Okay, now we're getting somewhere. This is actually a very helpful explanation.

So basically, the issue lies with the fact that when you attempt to define the photon's perspective, the time axis is reduced to zero length, or is undefined, due to the infinite length contraction of the universe which would be experienced at light speed. Essentially, there is nothing to view, and no time to view it in. I get that.

Maybe we shouldn't call it a "point of view", but it is how photons "experience" our universe. What do we do? Make up new words? Have entire conversations in quotations? Just ignore it?

Fredrik
Staff Emeritus
Gold Member

So basically, the issue lies with the fact that when you attempt to define the photon's perspective, the time axis is reduced to zero length, or is undefined, due to the infinite length contraction of the universe which would be experienced at light speed.
Yes, if we try to define it as the limit of a sequence of inertial frames, that's the sort of problem we run into. To be more precise, what happens in the limit v→∞ is that the x and t axes coincide (assuming that v is in the x direction).

The problem with the above is that it's not a valid coordinate system. It assigns the same coordinates to many points. Unlike the actual coordinate systems, such functions are not part of the mathematical structure that defines the theory, and they don't need to be.

Maybe we shouldn't call it a "point of view", but it is how photons "experience" our universe. What do we do? Make up new words? Have entire conversations in quotations? Just ignore it?
My previous post explained how to associate an inertial frame with the motion of an object that's moving with a constant velocity. If the object is a grid of rulers and synchronized clocks, the coordinates that the inertial frame assigns to each event agree with the measurements made by the rulers and clocks. This is why it makes sense to think of the co-moving inertial frame as representing the object's point of view.

One of the reasons why it doesn't quite make sense to think of a coordinate system in which a photon is stationary as the photon's point of view is that we can't imagine a grid of rulers and clocks that moves that way. We can't imagine a photon performing experiments and finding results that agree with the coordinate system that we have defined to be its point of view.

I'd rather not make up new words. I'm content with saying stuff like "event E has coordinates x(E) in coordinate system x". You can use any coordinate system you want. It doesn't have even have to be an inertial frame. Just make sure that what you're using is actually a coordinate system.

Yes, if we try to define it as the limit of a sequence of inertial frames, that's the sort of problem we run into. To be more precise, what happens in the limit v→∞ is that the x and t axes coincide (assuming that v is in the x direction).

The problem with the above is that it's not a valid coordinate system. It assigns the same coordinates to many points. Unlike the actual coordinate systems, such functions are not part of the mathematical structure that defines the theory, and they don't need to be.

My previous post explained how to associate an inertial frame with the motion of an object that's moving with a constant velocity. If the object is a grid of rulers and synchronized clocks, the coordinates that the inertial frame assigns to each event agree with the measurements made by the rulers and clocks. This is why it makes sense to think of the co-moving inertial frame as representing the object's point of view.

One of the reasons why it doesn't quite make sense to think of a coordinate system in which a photon is stationary as the photon's point of view is that we can't imagine a grid of rulers and clocks that moves that way. We can't imagine a photon performing experiments and finding results that agree with the coordinate system that we have defined to be its point of view.

I'd rather not make up new words. I'm content with saying stuff like "event E has coordinates x(E) in coordinate system x". You can use any coordinate system you want. It doesn't have even have to be an inertial frame. Just make sure that what you're using is actually a coordinate system.
Doesn't this mean that the speed of light is not only the limit for objects with mass, but for all possible reference frames as well? Even a hypothetical sub-luminal particle with zero mass would be prevented from achieving light speed due to the reference frame required to define it.

I've come across various speculative theories where it is suggested that space itself might be moved as a "pocket" at super-luminal speeds. I've always thought that sounded pretty implausible, and now that I understand the importance of a valid coordinate system, it seems absurd. Am I missing something there? Do proponents of such theories just take the super-luminal recession rates of distant galaxies, and misunderstand this as "space moving" at greater than c?

Well, for the distant galaxies it is more complicated. When you look at our Universe at large scales you cant assume that space is Pseudo-euclidean (like it is in SR). Well, space appears to be almost flat, but spacetime is not. Hence the expansion of the universe can not be described by SR, it must be described by GR because spacetime is curved. For more details check Cosmology forum, there are tons of topics about 'how galaxies can recede faster then c' - may be question #1 there :)

Well, for the distant galaxies it is more complicated. When you look at our Universe at large scales you cant assume that space is Pseudo-euclidean (like it is in SR). Well, space appears to be almost flat, but spacetime is not. Hence the expansion of the universe can not be described by SR, it must be described by GR because spacetime is curved. For more details check Cosmology forum, there are tons of topics about 'how galaxies can recede faster then c' - may be question #1 there :)
I know that. What I'm asking is whether the proponents of this "Space bubble" theory are using an incorrect interpretation of this process(inflation) to justify their premise. Or is it just a crackpot theory that bears no real examination? It seems that the dependence upon valid reference frames and coordinates would preclude this idea from holding any water.

There was an interesting thread there (dont remember the title), Marcus and someone else were discussing the 'expansion', and it appears that if you accept that distant objects just 'move away', then you get an inconsistent picture: the redshift of objects is inconsistent with their angle size.

Regarding your question, I dont understand. The Big bang theory is quite accurate. The WORDS used in this theory (expansion, galaxies accelerating away from us etc) are really misleading. But the worst is the BIG BANG itself which is not a BANG (so naive question #2 in Cosmology forum is 'where was a center of the Big Bang :) )

There was an interesting thread there (dont remember the title), Marcus and someone else were discussing the 'expansion', and it appears that if you accept that distant objects just 'move away', then you get an inconsistent picture: the redshift of objects is inconsistent with their angle size.

Regarding your question, I dont understand. The Big bang theory is quite accurate. The WORDS used in this theory (expansion, galaxies accelerating away from us etc) are really misleading. But the worst is the BIG BANG itself which is not a BANG (so naive question #2 in Cosmology forum is 'where was a center of the Big Bang :) )
I'm not sure why you're trying to explain inflationary theory to me. That's not what I'm questioning at all.

Fredrik's explanation of reference frames and coordinate dependence helped me to understand why we cannot mathematically describe the "Photon's Perspective". This lead me to question the validity of an idea which proposes that a "bubble" of space might be moved through regular space at faster-than-light speeds.

Since that idea seems ridiculous, I wondered if the proponents of said idea are somehow misinterpreting inflationary theory and applying it incorrectly.

Fredrik
Staff Emeritus
Gold Member

Doesn't this mean that the speed of light is not only the limit for objects with mass, but for all possible reference frames as well?
It's the limit for the set of inertial frames, but we are allowed to define and use coordinate systems that aren't inertial frames. A coordinate system is just a function $x:U\rightarrow\mathbb R^4$ where U is an open subset of spacetime. (There are some technical conditions as well. The most important one is that if x and y are coordinate systems, the function $x\circ y^{-1}$ which represents a change of coordinates, must be differentiable infinitely many times).

Even a hypothetical sub-luminal particle with zero mass...
That's a contradiction right there. Light speed is a mathematical consequence of zero mass.

That's a contradiction right there. Light speed is a mathematical consequence of zero mass.
I guess that was a poor choice of words on my part. I was trying to imagine an empty reference frame moving at light speed, and how that might work. That's just what I came up with to put in the center.

Ok let me address this as directly as I can. The photon moves at speed c according to you. And according to photon you move at speed c. For all practical purposes you are just another photon for the photon.

Yes, you have mass so you cannot move at c, but thats in your reference frame. But according to photon, you are a photon and so there is no contradiction there.

If you dont believe me, ask the photon

Fredrik
Staff Emeritus
Gold Member

Ok let me address this as directly as I can. The photon moves at speed c according to you. And according to photon you move at speed c. For all practical purposes you are just another photon for the photon.
Not at all. A massless particle's motion is represented by a null curve, and a massive particle's motion is represented by a timelike curve. The properties of being "null" or "timelike" have nothing to do with coordinates, so a change of coordinates can't change a timelike curve to a null curve.

Also, if we choose to define the photon's rest frame (I'm emphasizing the choice because you still seem to think it defines itself without any choices made by us) in such a way that I'm moving with speed c in those coordinates, you may be not moving with speed c in those coordinates.

We don't try to imagine how a photon experienves the universe because it doesn't experience the universe. because of the time dilation effect at velocity c from the reference frame moving at c, no matter how long any other refrence frame experiences the event of motion at c, the frame moving at c experiences no time at all. therefore a photon, from its own point of view, exists instantaneously and therefore does not experience the universe. thats basically just another way of stating what Fredrik said.

I've seen plenty of comments on why OB50's line of thinking shouldn't be done. So what? Is the point not to look behind the curtain because you cannot see how to lift it, and so encourage others to go play somewhere else?

It's very fine to learn physics as it is known. But if physics were a stagnant set of rules I would have nothing--nothing at all--to do with it. Perhaps I'm wrong, but I think I share this with most of you.

Though I don't propose this is OB50's line of thinking, you might consider the following hubris, running somewhat in parallel.

..."Einstein wrote that it was in that same year, at age 16, that he first performed his famous thought experiment visualizing traveling alongside a beam of light (Einstein 1979)." -wikipedia

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