Reconciling Light's Perspective: The Flaw in Relativity?

[kamikaze762]

I am confused as to why a photon's view is such a meaningless concept when we can obviously measure the speed of the photon from our own reference frame. We see the photon moving through spacetime, so why can't we theorize on how the photon sees us?

Is there is flaw in relativity? It seems counter-intuitive to state that light has a definite speed, that there are no preferred frames, yet we can measure one frame relative to us but looking at from the other side is meaningless...

Perhaps my logic is getting a little blended here, but I, as an observer, see light moving. It has a speed, it occupies a position, and I see it taking time to move. Why can we not take a ride on a photon and see how things look?

 

[Eynstone]

I am confused as to why a photon's view is such a meaningless concept when we can obviously measure the speed of the photon from our own reference frame. We see the photon moving through spacetime, so why can't we theorize on how the photon sees us?

That's the very question that led Einstein to relativity - 'what if I run alongside of a light wave?' . If someone rode a photon, it would be at rest in his frame of reference ,contrary to the postulate of relativity.

 

[matheinste]

I am confused as to why a photon's view is such a meaningless concept when we can obviously measure the speed of the photon from our own reference frame. We see the photon moving through spacetime, so why can't we theorize on how the photon sees us?

Is there is flaw in relativity? It seems counter-intuitive to state that light has a definite speed, that there are no preferred frames, yet we can measure one frame relative to us but looking at from the other side is meaningless...

Perhaps my logic is getting a little blended here, but I, as an observer, see light moving. It has a speed, it occupies a position, and I see it taking time to move. Why can we not take a ride on a photon and see how things look?

To put it crudely, to make measurements we need a coordinate system (frame of reference ). It is usually simpler to have a coordinate system in which we are at rest and for a timelike vector representing our motion we can always tranform to a system in which we are at rest. The photon does not have a frame in which it is at rest or one which can be transformed into such a frame. So we cannot lay down a coordinate system from which a photon can make measurements.

Matheinste.

 

[Fredrik]

I am confused as to why a photon's view is such a meaningless concept when we can obviously measure the speed of the photon from our own reference frame. We see the photon moving through spacetime, so why can't we theorize on how the photon sees us?

When we talk about your point of view, we have something very specific in mind: an assignment of coordinates based on a specific procedure that involves emitting light and seeing it come back to you after a reflection somewhere else. A massless particle like a photon doesn't have a "point of view" because this procedure wouldn't work. Even if light could emit light, it wouldn't come back after a reflection.

Is there is flaw in relativity? It seems counter-intuitive to state that light has a definite speed, that there are no preferred frames, yet we can measure one frame relative to us but looking at from the other side is meaningless...

Lots of things in relativity are counterintuitive. Does every one of them make you think there's a flaw in relativity?

Perhaps my logic is getting a little blended here, but I, as an observer, see light moving. It has a speed, it occupies a position, and I see it taking time to move. Why can we not take a ride on a photon and see how things look?

I answered that above, and in more detail in the quote below. The closest thing to "taking a ride on the photon" that you can do is to consider a massive particle's point of view and take the limit v→c. But there's no good reason to call the result "a photon's point of view". The result of this procedure isn't an inertial coordinate system (as it would be for every massive particle). In fact, it's not a coordinate system at all, since it doesn't satisfy the usual mathematical requirements.

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?

 

[bcrowell]

FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

 

[kof9595995]

Although I'm 99.99% convinced photon can't be used as a reference frame , I always wonder what if there exists some creature solely made up by photons, what will the world look like in that creature's eyes.

 

[bcrowell]

Although I'm 99.99% convinced photon can't be used as a reference frame , I always wonder what if there exists some creature solely made up by photons, what will the world look like in that creature's eyes.

The argument in the final paragraph of #5 holds regardless of whether there is an observer or not.

 

[kof9595995]

The argument in the final paragraph of #5 holds regardless of whether there is an observer or not.

I agree with the "one-to-one" part, but if you invoke Lorentz transformation formula, i think the resoning given in post 2 is good enough, after all Lorentz transformation formula is derived from the constancy of speed of light. Anyway it doesn't help to stop me wondering why a photon obsever is forbiden.(i'm not implying SR is wrong, but it is really a mystery to me why such a observer is forbiden since there exsits something traveling at speed of light)

 

[yuiop]

Note: The conventional view is that an inertial reference frame can not have a relative velocity equal to the speed of light and a photon can not have a point of view. I agree with that, but this question comes up so often here, that I am for a moment going to "look outside the envelope" in this post and see if it helps anyone.

That's the very question that led Einstein to relativity - 'what if I run alongside of a light wave?' . If someone rode a photon, it would be at rest in his frame of reference ,contrary to the postulate of relativity.

Let us use the relativistic velocity addition equation

$$w = \frac{v+u}{1+uv/c^2}$$

and see what it has to say.

In that equation v is the velocity of observer1 wrt observer2 and u is the velocity of a particle wrt observer1. W is the velocity of the particle relative to observer2. Now if observer1 has a velocity of v=c and the velocity of a particle moving relative to him is also the speed of light (u=c), then:

$$w = \frac{c+c}{1+c^2/c^2} = c$$

So the velocity of particle moving at c relative to observer1, who is moving at c relative to observer2, is still c from the point of view of observer2.

Now let us reverse the equation and determine the velocity (u) of a particle from the point of view of observer1, that has velocity w=c from the point of view of observer2.

$$u = \frac{w-v}{1-wv/c^2} = \frac{c-c}{1-c^2/c^2} = \frac{0}{0}$$

Now 0/0 is indeterminate and that pretty much demonstrates that a photon does not have a point of view about the velocity of any other particle.

 

[bcrowell]

I agree with the "one-to-one" part, but if you invoke Lorentz transformation formula, i think the resoning given in post 2 is good enough, after all Lorentz transformation formula is derived from the constancy of speed of light.

There are various ways of deriving the Lorentz transformation. There are some derivations that start with constancy of c as an axiom, but there are others that don't, e.g., Morin (2008).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008, Appendix I

 

[bcrowell]

Anyway it doesn't help to stop me wondering why a photon obsever is forbiden.(i'm not implying SR is wrong, but it is really a mystery to me why such a observer is forbiden since there exsits something traveling at speed of light)

Yeah, it is a little surprising that you can prove, based on such fundamental considerations of SR, that you can't have an observer who is made out of massless particles and who travels at c.

If you want to see more explicit reasons, I don't think think it's hard to come up with some fairly direct reasons that it would be implausible for such an observer to exist.

If this observer is to have the point of view of moving at c, then he probably has to have his entire body moving at c, all in the same direction. (After all, there are photons inside my body at the moment, but their center of mass is not moving at c relative to my desk.) If the observer consists of a cloud of photons all moving along parallel lines, then it starts to sound like the photons aren't interacting with one another. So how do you get a conscious observer out of a cloud of noninteracting particles?

I think you also get issues with the arrow of time. A photon always has constant proper time, whereas an observer would presumably have to have a psychological arrow of time, so that it can be said to increase its knowledge after a measurement.

 

[kof9595995]

Thanks bcrowell! It's nice to learn stuff from you

I think you also get issues with the arrow of time. A photon always has constant proper time, whereas an observer would presumably have to have a psychological arrow of time, so that it can be said to increase its knowledge after a measurement.

This part I'm not sure what you were trying to say, can you elaborate a bit more?

 

[kof9595995]

There are various ways of deriving the Lorentz transformation. There are some derivations that start with constancy of c as an axiom, but there are others that don't, e.g., Morin (2008).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008, Appendix I

I checked the Appendix I of this book, but it seems Morin also used the constancy of light in the derivation.

 

[yuiop]

... but it is really a mystery to me why such a observer is forbiden since there exsits something traveling at speed of light)

I hope the other members will allow me some "poetic licence" in answering this question because strictly speaking we are talking about an unphysical situation.

From the "point of view of a photon" everything parallel to its direction has zero length so the entire universe is contracted to a 2 dimensional plane at right angles to its direction. This plane has zero thickness and therefore zero volume, so nothing is "visible" and the universe appears empty. Time dilation means that to an observer moving at the speed of light, everything else appears frozen in time and so a photon has no sense of space or time. On the other hand you could argue that if a photon had an internal clock it would be stopped and so the everything seems to happen at the same time. This contradicts the everything should appear frozen point of view so it becomes clear that the "point of view of a photon" does not make sense.

 

[Ich]

Yeah, it is a little surprising that you can prove, based on such fundamental considerations of SR, that you can't have an observer who is made out of massless particles and who travels at c.

(emphasis mine)
kof9595995 didn't ask about such an observer. He asked about "some creature solely made up by photons", and I see no reason why such an observer should be forbidden.
At least that's my interpretation of the question.

 

[Vanadium 50]

Although I'm 99.99% convinced photon can't be used as a reference frame , I always wonder what if there exists some creature solely made up by photons, what will the world look like in that creature's eyes.

Bright. Very bright.

 

[bcrowell]

I checked the Appendix I of this book, but it seems Morin also used the constancy of light in the derivation.

I believe he does it both ways, and I think the material may be spread around in different places in the book. You may have to dig around a little bit in order to find it.

 

[bcrowell]

(emphasis mine)
kof9595995 didn't ask about such an observer. He asked about "some creature solely made up by photons", and I see no reason why such an observer should be forbidden.
At least that's my interpretation of the question.

I think his motivation for asking about such a creature was that it seemed to him that such a creature might constitute an observer whose reference frame would be moving at c.

 

[netheril96]

There is no reality beyond measurement.
Since you can never measure the world with the speed of light,it is totally meaningless to consider the reference frame with speed of c.

Things that can neither be tested for or against is NOT science.That is philosophy.

 

[kof9595995]

There is no reality beyond measurement.
Since you can never measure the world with the speed of light,it is totally meaningless to consider the reference frame with speed of c.

Things that can neither be tested for or against is NOT science.That is philosophy.

I don't think my question is pure philosophical and beyond all measurements, let's say the photon creature exists, it can record what it "sees", then if we can extract what it recorded as a piece of information, then we did measure the world in with the speed of light.
Well,maybe there should be some mechanism to prevent such creature existing or us extracting the information recorded by the creature. But anyway i couldn't come up with any mechanism like that from the physics I learnt.

 

[bcrowell]

Since you can never measure the world with the speed of light

What we've been discussing is the justification for this statement. For the reasons discussed in posts 6, 7, 8, and 11, this assertion isn't quite as obvious as you seem to believe.

I think you also get issues with the arrow of time. A photon always has constant proper time, whereas an observer would presumably have to have a psychological arrow of time, so that it can be said to increase its knowledge after a measurement.

This part I'm not sure what you were trying to say, can you elaborate a bit more?

Which step is unclear to you?

 

[kof9595995]

A photon always has constant proper time

Here did you mean that photon's proper time is always 0?

A photon always has constant proper time, whereas an observer would presumably have to have a psychological arrow of time so that it can be said to increase its knowledge after a measurement.

"an observer would presumably have to have a psychological arrow of time so that it can be said to increase its knowledge after a measurement." This part is clear, but i don't know why you emphasized "A photon always has constant proper time" at the beginning of the sentence. What were you trying to deliver?

 

[bcrowell]

A photon always has constant proper time.

Here did you mean that photon's proper time is always 0?

I think we need to distinguish between s and ds here. ds=dt^2-dx^2 is always zero for a photon. Integrating, we find that s is always a constant for a photon.

"an observer would presumably have to have a psychological arrow of time so that it can be said to increase its knowledge after a measurement." This part is clear, but i don't know why you emphasized "A photon always has constant proper time" at the beginning of the sentence. What were you trying to deliver?

If the proper time is always constant, then there is no arrow of time. If there is no distinction between future and past proper time, then there can be no concept of having more information in the future than in the past.

 

[kof9595995]

Thanks, now i see your point