Exploring the Motion and Dimensions of Light in General Relativity Theory

[Lyuokdea]

Was just thinking about this earlier today. Digging through a couple books, I haven't found an obvious statement one way or the other.

GR tells us that light waves move along lines of equal proper time ([tex]d\Tau = 0[\tex]). Furthermore, an observer traveling with the beam of light would experience instantaneous motion from point a to point b because length contraction would render the distance between the two points to 0.

Is this equivalent to saying that light waves exist in a two dimensional projection of the universe, with the dimension along the line of sight being compressed to 0?

The equivalence between the two statements may be of only philosophical importance, but, if correct, it seems to be an easy way to imagine the physics of light.

~Lyuokdea

 

[Dale]

http://www.edu-observatory.org/physics-faq/Relativity/SpeedOfLight/headlights.html

 

[Crazy Tosser]

You could say that from the photon's frame of reference it is everywhere in the universe. I would probably go as far as saying that from the photon's frame, it is the only thing in the universe - that's why many physicists argue that a photon doesn't have a frame of reference xD. Frame of reference of a photon is... meaningless...

 

[JesseM]

You could say that from the photon's frame of reference it is everywhere in the universe.

A photon does not have its own frame of reference in relativity. See DaleSpam's link.

 

[Crazy Tosser]

A photon does not have its own frame of reference in relativity.

Whatever makes you so certain?

And the link... ah, the link... I could write something very similar and post it online... only proving that photons are actually tiny penguins whose wing flapping creates electromagnetic fields. A link is not an authority - not that anything is.

 

[JesseM]

Whatever makes you so certain?

Among other things, it would violate the first postulate of SR, which says that the laws of physics must work the same way in all inertial reference frames. A photon cannot be at rest in any sublight reference frame.

There's also the fact that the coordinates of an inertial reference frame are defined in terms of rulers and clocks at rest in that frame, and it would be impossible to accelerate a ruler or clock to the speed of light (and even if you consider the limit as they approach the speed of light, the rulers would approach being shrunk to zero length and the clocks would approach being completely frozen, so they'd be useless for defining a coordinate system).

 

[Primordial]

If it does not have a frame of reference, then how can its period be relativistic to an inertial reference.

 

[atyy]

Is this equivalent to saying that light waves exist in a two dimensional projection of the universe, with the dimension along the line of sight being compressed to 0?

I don't think so, at least not exactly. However, the "light front" is a 3D "null hypersurface" in 4D spacetime. For simplicity, people usually draw only 2 of the 3 dimensions of a null hypersurface. Sometimes people use null hypersurfaces to construct coordinates. In special relativity, such coordinates are not inertial, as pointed out by DaleSpam and JesseM. In general relativity, apart from constructing coordinates, a special type of null hypersurface is the event horizon of a black hole.

http://www.saha.ac.in/theory/a.harindranath/light/light.html
http://arxiv.org/abs/gr-qc/0503113

 

[jtbell]

If it does not have a frame of reference, then how can its period be relativistic to an inertial reference.

I'm sorry, I don't understand this question. Can you expand it or phrase it in other words?

 

[Naty1]

Is this equivalent to saying that light waves exist in a two dimensional projection of the universe, with the dimension along the line of sight being compressed to 0?... it seems to be an easy way to imagine the physics of light.

Absent the fact that there is no rest frame for light in relativity, let's assume your statement IS reasonable...
what conclusions, what insights, what simplifications arise?? ...How might you explain gravity curving the path of light, for example?

 

[inquisitive_i]

mass of light

with all due respesct...
theory of relativity suggests that light rays must bend owing to the gravitational field..
i take it as light rays are attracted by gravitational force, however, Newton's law suggests that gravity is a property of mass (GMm/r^2)..
but photons are massless particles.. so it poses a contradiction..
please expalin..

 

[jtbell]

In general relativity, gravitation is a manifestation of the curvature of spacetime. The motion of all objects is affected by this curvature, regardless of whether they have mass or not. Light follows geodesic paths in spacetime, which are straight lines in flat spacetime, and curved paths in curved spacetime.

I suppose Newton's law of gravitation emerges from Einstein's field equations of general relativity when you apply them to a system of two massive objects and make suitable approximations.

 

[inquisitive_i]

so does that mean that light travels straight but space is curved due to gravity..?

well i'll agree with it jtbell but than.. question comes that what kind of bending occurs in space in the case of a black hole where light coming out of it is engulfed by itself..

 

[Dale]

And the link... ah, the link... A link is not an authority

The usenet physics FAQ is a very reputable and reasonably authoritative source. The information there is as good as anything other than peer reviewed journals, which usually charge for access. It is certainly much more credible than anything from some random poster on an internet forum.

The reason I simply post the FAQ link is because this question shows up here at least weekly and is therefore a Frequently Asked Question and should have a link to a good FAQ as the response.

 

[Primordial]

jtBell : I think the photon must have a frame of reference in time, allowing interaction with the relativistic aspect of inertial reference systems. The only relativistic effect I know of relative to an inertial reference a photon may have, is a change in its relative period that determines its relative mass or energy and does not affect the relative rate of propagation through space-time. Thank you for your time.

 

[JesseM]

jtBell : I think the photon must have a frame of reference in time, allowing interaction with the relativistic aspect of inertial reference systems.

Do you understand that an object's "reference frame" just means a coordinate system where the object is at rest (i.e. in this coordinate system, its x, y, z coordinates don't change when the t coordinate increases), and that we can analyze the behavior of any object using whatever coordinate system we please, we don't ever need to use the object's own rest frame to predict how it will interact with other objects? This is just as true for objects moving slower than light as it is for photons (for photons there is no inertial reference frame where they are at rest, although it would be possible to construct a non-inertial coordinate system where a photon is at rest, though the equations for the laws of physics aren't the same in non-inertial coordinate systems as they are in inertial ones).

 

[Primordial]

JesseM : If the photon exists at all spatial points in a system, would it not be at rest.

 

[JesseM]

JesseM : If the photon exists at all spatial points in a system, would it not be at rest.

You're imagining a coordinate system where the photon exists at multiple spatial coordinates at a single time coordinate? This would not be a "rest frame" for the photon, and again, when physicists talk an object's "own frame" they are always talking about its rest frame. This is not to say you couldn't construct a non-inertial coordinate system with the property you describe, but what would be the point exactly?

 

[Primordial]

JesseM :I'm trying to separate the initial energy of each photon relative to another and allow the photon to exist in all spatial dimensions (not limited by Planck time), by this I can allow large photons to exist past the relativistic mass allowed with Planck limitations. I think photons and other bosons interact within their proper time dimension. I just want to know what happens when photons above gamma, but with a period very near Planck time is pushed into, or past Planck minimum time in an event with matter, and how it would react according to relativity. I know this sounds far out and apologize if I cause problems. Thank you for you response.

 

[JesseM]

JesseM :I'm trying to separate the initial energy of each photon relative to another

"Separate" what from what? And "initial" referring to what event? And energy is a frame-dependent quantity, what frame are you using to define it? If it's a non-inertial frame you need to give an explicit equation for how you define "energy" in that frame in order for statements about energy to be meaningful.

and allow the photon to exist in all spatial dimensions (not limited by Planck time), by this I can allow large photons to exist past the relativistic mass allowed with Planck limitations.

What "planck limitations" do you mean? Special relativity has nothing special to say about the Planck scale, and neither do existing quantum field theories, it's only in speculations about quantum gravity that the Planck scale takes a special role. And what does "allowing the photon to exist in all spatial dimensions" have to do with relativistic mass?

I think photons and other bosons interact within their proper time dimension.

Proper time is not a "dimension" unless you have a coordinate system with proper time as one of the axes. And this would make little sense in the case of a photon since there are no differences in proper time between events on their worldline.

I just want to know what happens when photons above gamma

"Above gamma"? Gamma is defined as $$\frac{1}{\sqrt{1 - v^2/c^2}}$$, if you try to plug in v=c for a photon you would get gamma = infinity, how can you go above that?

but with a period very near Planck time is pushed into

"Period" of what? Are you talking about "period" in the sense of 1/frequency or are you just talking about a period of time between some pair of events?

or past Planck minimum time in an event with matter

What kind of "event with matter"? Sorry to ask so many questions but basically nothing you've said makes any sense to me.

 

[Primordial]

Jessem : I apologize for wasting your time. I wish I could explain it better but that's the best I can do for now. It's hard for me to see the possibility of a photon having infinite relativistic mass. I think the photon has a limit for its relativistic mass. Thank you for your time.

 

[JesseM]

Jessem : I apologize for wasting your time. I wish I could explain it better but that's the best I can do for now. It's hard for me to see the possibility of a photon having infinite relativistic mass. I think the photon has a limit for its relativistic mass. Thank you for your time.

A photon doesn't have an infinite relativistic mass in SR. relativistic mass = gamma * rest mass, and the photon has a rest mass of 0, so even if you assume gamma = infinity this doesn't give a relativistic mass of infinity, it just gives an undefined relativistic mass. However, we also have the formula Energy = relativistic mass * c^2, so you could also define relativistic mass as Energy / c^2, and a photon does have a well-defined (and finite) energy--in quantum physics it's just E = hf, where h is Planck's constant and f is the frequency.

 

[inquisitive_i]

In general relativity, gravitation is a manifestation of the curvature of spacetime. The motion of all objects is affected by this curvature, regardless of whether they have mass or not. Light follows geodesic paths in spacetime, which are straight lines in flat spacetime, and curved paths in curved spacetime.

I suppose Newton's law of gravitation emerges from Einstein's field equations of general relativity when you apply them to a system of two massive objects and make suitable approximations.

thanx jtBell..
but the question comes that what kind of bending occurs in space in the case of a black hole where light coming out of it is engulfed by itself..

 

[Primordial]

JesseM : I apologize for having to run. The relativistic effect I was referring to, was blue shift in photons that exist in the initial energy range well above the gamma photon. The event I am choosing is one where the photon would meet the relativistic wave length and relativistic mass that would satisfy the necessary relativistic mass and the necessary one half wave length of the described photon that will meet the schwarzschild equation for a black hole. I was wondering could this in your opinion limit the relativistic limit to relativistic mass for a photon? Thank you for your response. Sorry about having to exit.

 

[JesseM]

JesseM : I apologize for having to run. The relativistic effect I was referring to, was blue shift in photons that exist in the initial energy range well above the gamma photon.

What do you mean by "the gamma photon"? Do you mean a photon with a frequency in the gamma range of 10^19 cycles per second or higher? I had assumed that when you talked about "gamma" you meant the relativistic gamma-factor $$\frac{1}{\sqrt{1 - v^2/c^2}}$$ which is unrelated to the gamma frequency range. But if you were talking about the gamma frequency range, I still don't understand why you said the relativistic mass would be infinite--like I said, relativistic mass can be definced as E/c^2, and for a photon the energy is given by E = hf, where h is Planck's constant and f is the frequency. So, no matter how large the frequency, as long as it's a finite number the energy E will be finite too, and so will be the "relativistic mass" defined by E/c^2.

The event I am choosing is one where the photon would meet the relativistic wave length and relativistic mass that would satisfy the necessary relativistic mass and the necessary one half wave length of the described photon that will meet the schwarzschild equation for a black hole. I was wondering could this in your opinion limit the relativistic limit to relativistic mass for a photon? Thank you for your response. Sorry about having to exit.

In quantum gravity I imagine there might be a lower limit on the wavelength (perhaps just the Planck length?), which would mean an upper limit on the frequency (which is just c/wavelength), which would mean an upper limit on the energy (and relativistic mass E/c^2) because of the equation E=hf. If the lower limit on wavelength was precisely equal to the Planck length, for example, that would imply that upper limit on energy was equal to 2pi*the Planck energy (see Planck units). Is this the sort of thing you're asking about?

 

[Primordial]

JesseM : Yes that is what I'm working on, and thank you for answering my question.