The Photon's Perspective Taboo

[ilocar]

I completely agree with fredrik on this one, the math doesn't purport any possibe rest frame for a particle of 0 mass. and sorry about the limit, I was of course taking a limiot but I;m not used to telling everyone when the math comes out with infinity. I always forget limits in this sort of case because I feel an infinity implies that a limiot has been taken. plus we haven't taken in limit in my calculus class since before christmas, excuse me if I'm a little rusty.
the way I see the "photon's perspective" from a purely qualitative and phiosophical standpoint is that for an instant, dt if you will, a photon experiences all matter in every location it will ever be, basically its existence is condensed into so short a time that every moment pancaked on top of the next. if you imagine state space like a long cylinder, whose circular cross-sections are instantaneous states of the universe. because the photon is moving at c all those cross-sections are crushed into a 3-dimensional lamina, so basically the photon, and other particles of mass 0, experiences a purely 3-dimensional universe. those are just my thoughts you can agree or not, if there is some flaw in my logic or understanding of special relativity, feel free to call me a moron :)

 

[OB 50]

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

Actually, that's pretty much why I brought this up. I suspect that there is a lot yet to be learned from the unique behavior of light, yet it is rarely discussed from this angle.

OB50, how do you reconcile the existence of a rest frame for a photon with the second postulate of special relativity?

I don't.

Yet, here we are with a particle(wave) that moves from point A to point B at a certain speed. We can naively imagine this happening with ease. From Sun to Earth: 8 minutes. It doesn't seem so completely impossible on its face, but the math breaks down and the universe won't allow it to happen.

It seems like this might be one of present-day physics' "blind spots." Do I have a well-formed theory based on anything specific? No. Do I think that there is the potential for useful discussion and discovery surrounding this concept? Definitely.

 

[DaveC426913]

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?

It might be more useful to think of a photon as a static line segment joining two points in spacetime. It has two endpoints, both probably buried in electron orbitals. One end the of segment is farther along the time dimension than the other. The photon does not move through time, it does not experience time, it is just a line segment.

 

[Naty1]

Post 27 above is right on..."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.."

I did not see any other posts that recognize general and special relativity are approximations...as are all quantum theories so far...we should encourage people to look at things in different ways, say from the perspective of a photon, because remaining contrained by current theories and even current mathematical formulations is unlikely to result in improved theories.

Einstein REJECTED fixed notions of space and time and Newton's theory of gravity...and he had the insight to draw upon theories of mathematics that were NOT in mainstream use at the time...had he not done so he would have never achieved an improved theory of gravity...

The above posts that explain "it makes no sense" blah blah blah should ring a huge bell of alarm! If we can't explain all points of view, something is wrong! We seem to have acheived better insights in some respects regarding frames of reference for black holes than photons: a remote stationary observes an event horizon; a free falling observer moving through such an apparent horizon sees no such thing...and from the perspective of the remote stationary observer, the free falling observer remains at the event horizon for an infinite time...while the free falling observer plunges through and is torn asunder...those are crazy comments, but apparently understood currently as resulting from different frames of reference...

finally, since GR is an approximate theory, don't be so smug that "c" is the maximum speed achievable...unanticipated (impossible?) surprises are what physics is all about...for now I can accept "c" as conventionally understood, but I expect 1000 generations from now scientists will laugh at the beliefs of today...I sure hope so...who would have guessed even "scientific" 25 years ago that 96% of the matter and energy in the universe is completely unknown?

 

[Dale]

Do I have a well-formed theory based on anything specific? No. Do I think that there is the potential for useful discussion and discovery surrounding this concept? Definitely.

This is fine, but if you want to move your idea from something potentially useful to a well-formed theory then you should listen to atyy and Frederik's advice.

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.

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)?

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.

Essentially, the take home message of these posts are that you can construct any number of coordinate systems in which a photon is at rest. They are all non-inertial, but at least they are valid coordinate systems, unlike the standard definition of an object's "perspective" erroneously applied to a photon.

I would encourage you to go ahead and learn how to properly use non-inertial reference frames. You can then take that knowledge and really describe physics from any number of coordinate systems where a photon is at rest.

 

[Phrak]

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

OB50, sometimes the hard part is formulating the right question. Or approch the problem from first formulating some useful questions. Dale seems to know the right question.

It could go something like this. What is the transformation from coordinates X to coordinates X', where v-->c? v is the velocity of the orign of X' in coordinates X.

Next map a photon--a wave or a particle, from one coordinate system to the another. Does this help?

 

[stillwonder]

A question should be answerable in at least same terms as it is put in. So if OP has asked a mathematically non rigorous question, the answer should be that much at the minimum.

Physics will have the last word, but that also means someone needs to have the first word. Thats where OP comes in.

 

[Dmitry67]

BTW the inexistence of a photon rest frame has some direct physical consequeces, for example, e+ + e- -> gamma (electron and positron annihilate forming only one photon) is impossible because there is no frame where gamma is at rest (while there is such frame for the center of mass of e+ and e-)

 

[Phrak]

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.

Nevertheless, a coordinate system can be constructed.

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).

I can see no a priori reason to discount coordinate maps that are not infinitely differentiable nor, for that matter, noninvertible. To derive some properties of a coordinate system whos origin has a relative velocity, v→c to an inertial coordinate system, it is sufficient, and apparently necessary to consider those that are neither.

By maps, I am referring to the composition, z = x\circ y^{-1}, and it inverse, z^-1,

Some of it overlaps with some of what I said, but at the very least I said a lot more than that. And I really wouldn't talk about "the time dilation effect at velocity c from the reference frame moving at c". You can't just set v=c and expect things to remain well-defined. You have to talk about the limit v→c instead.

OK by me.

 

[atyy]

Nevertheless, a coordinate system can be constructed.

Yes, I agree, so it's not "nevertheless".

 

[Phrak]

Yes, I agree, so it's not "nevertheless".

Everthemore?

 

[atyy]

Everthemore?

 

[Phrak]

http://img14.imageshack.us/img14/8451/perspectiveofaphoton.jpg

 

[DaveC426913]

Translation? The photons maps to anywhere/everywhere in the universe?

The problem I have with provding a mathematical solution is that it is wide open to being interpreted semantically. i.e. contributors are now free to describe the photon's "experience" by metaphorizing the math as they see fit.

 

[Phrak]

Translation? The photons maps to anywhere/everywhere in the universe?

Thanks for responding, Dave. In the (a',b',x',y') coordinate system, the orign of (a,b,x,y), and therefore (ct,x,y,z) as well, would be smeared over the b' axis.

The temptation is to construct a primed Minkowski space (ct',x',y',z'), with the usual metric. But this doesn't follow immediately, that I can see. The points in (a',b') are a topological points space; a metric would be an addition premise, which would be overly speculative, etc, etc.

The problem I have with provding a mathematical solution is that it is wide open to being interpreted semantically. i.e. contributors are now free to describe the photon's "experience" by metaphorizing the math as they see fit.

I agree. Though, in the OP's defense, until you know the question you need to ask, how do you ask the question? The title I used was the filename I chose give by the name of this thread.

I am answering the question, "what is the coordinate system where v_x --> c". To be strict, it appears not a coordinate system but a topology.

You seem to be concerned about infringing on the PF rules, but there is no new theory here, just special relativity, unless I've made an error.

A photon is an extended object isn't it? One needs a family of coordinate transforms.

btw, have I taken any liberties with the meaning of limits?

 

[Phrak]

Translation? The photons maps to anywhere/everywhere in the universe?

Maybe you meant a beam of light traveling in the x direction. The beam lies along the a axis. This maps to a'=0. b is spread all over finite b', and y'=y=0, z'=z=0. Nothing can be said about x' and t' without premising a metric (I think), if it's even meaningful to do so. Is that what you meant? The x and t coordinates remain what they were, the line segment x=ct, lying on the light cone.