A photon always travels in a black hole

[Koning_D]

TL;DR

Length contraction creates black hole around photon

A photon travels at the speed of light. This means, by length contraction, for him the length of the universe in the direction he travels is zero. This means that all the masses on his trajectory are concentrated at the point of the photon. Considering the size of the universe and the distribution of mass in it, chances are big that the sum of all these masses will create a black hole, with the photon right in the centre of it. Since nothing can escape a black hole, how come we see light?

 

[PeroK]

TL;DR Summary: Length contraction creates black hole around photon

A photon travels at the speed of light. This means, by length contraction, for him the length of the universe in the direction he travels is zero. This means that all the masses on his trajectory are concentrated at the point of the photon. Considering the size of the universe and the distribution of mass in it, chances are big that the sum of all these masses will create a black hole, with the photon right in the centre of it. Since nothing can escape a black hole, how come we see light?

Length contraction is a coordinate effect associated with inertial references frame (in which the laws of Special Relativity apply). The rest frame of a photon is not an inertial reference frame. More precisely, two inertial references frame must be related by a sub-luminal speed.

In any case, length contraction and time dilation are coordinate effects. A black hole is a physical phenomenon that cannot be created simply by considering relative motion.

 

[Ibix]

This means, by length contraction, for him the length of the universe in the direction he travels is zero.

No. Your mistake is assuming that results derived for relationships between inertial reference frames also apply to whatever coordinate system you are using where light is at rest. Such systems can be constructed but they are not inertial reference frames. Thus you are wrong to think that length contraction is a relevant concept here.

The rest of your reasoning is based on this error, so the final question doesn't really make sense.

 

[Dale]

TL;DR Summary: Length contraction creates black hole around photon

Considering the size of the universe and the distribution of mass in it, chances are big that the sum of all these masses will create a black hole

In addition to what others have said, this logic also fails. In the frame you are describing, the energy density is large. But the momentum density is also large.

The source of gravity is the entire stress energy tensor including both energy and momentum densities. For the purpose of black hole formation the momentum density roughly cancels out the energy density. So a black hole will not form in a frame where an object is moving if it doesn’t form in a frame where the object is at rest.

 

[pervect]

Photons don't have a point of view, there is no frame of reference for a photon. There used to be a FAQ about this, but I couldn't find it. I'm not so active these days, perhaps one of the moderators or other posters can find and post the link. I looked with search, without success - and I thought it was sticky and near the top, but I didn't see any such sticky threads.

Assuming a photon has a point of view leads to various contradictions and false statements, because the assumption is fundamentally incorrect and not self-consistent.

The FAQ probably worded it better, but the reason "photon's" don't have a point of view is because there is no frame of reference in which a photon is at rest, as by definitions photons always move at the speed of light. Assuming that photons move at the speed of light, and also do not move at all (which is implied by the notion of a frame of reference) leads to errors, of which your conclusion that a photon must be a black hole is an example of. Note - "photons" in this context are classical, but massless particles that move at the speed of light, SR/GR is not a quantum theory, the quantum notion is different.

It is possible to construct coordinate systems in which the coordinate of a "photon" is constant, such as taking (t,x,y,z) as minkowskii coordinates, and then doing a coordiante transformation from (t,x,y,z) to (s,x,y,z) where s = t - x/c. Such generalized coordinates are not, however, a standard "point of view", they can be studied mathematically with the proper tools however.

Its possible to do physics without using coordinates at all. The best reference I could find on Wiki discussing the basic concepts was https://en.wikipedia.org/wiki/Coordinate-free. In fact, studying the coordinate free (or covaraint) methods of physics is probably the best way to appreciate how to do physics with generalized coordinates. However, this is an A-level topic, and the wiki article may be too advanced. But I felt I should at least mention the topic. It's also a personal favorite, which may be biasing my decision.

Wiki points out the advantages of coordinate free methods in avoiding conceptual mistakes such as the one in this thread:

Coordinate-free treatments generally allow for simpler systems of equations and inherently constrain certain types of inconsistency, allowing greater mathematical elegance at the cost of some abstraction from the detailed formulae needed to evaluate these equations within a particular system of coordinates.

This historical note is also interesting. As wiki points out, we do Euclidean geometry without coordinates all the time.

Coordinate-free treatments were the only available approach to geometry (and are now known as synthetic geometry) before the development of analytic geometry by Descartes.

 

[Nugatory]

The FAQ is https://www.physicsforums.com/threads/rest-frame-of-a-photon-faq-by-forum-members.511170/ and linked from a sticky at the top of the page: https://www.physicsforums.com/threa...hotons-gravity-time-dilation-and-more.807523/

But @pervect's answer is more complete than the FAQ.

 

[PeterDonis]

Its possible to do physics without using coordinates at all.

The classic exposition of the coordinate-free viewpoint in the context of relativity is of course Misner, Thorne, & Wheeler's textbook. The "centrifuge and photon" example early in the book is a good illustration of the advantages of the coordinate-free viewpoint.

 

[Koning_D]

Thank you all! I knew there had to be something wrong in my chain of thoughts. It appears the real implications of SR are way over my head. Maybe I'd better stick to GR. ;-)

 

[PeroK]

Thank you all! I knew there had to be something wrong in my chain of thoughts. It appears the real implications of SR are way over my head. Maybe I'd better stick to GR. ;-)

The point is that length contraction is a coordinate effect. If someone moves past the Earth at relatively near light speed, you don't change. Your body continues to function exactly as it did before they began to "observe" you at high relative speed. There is no sense in which you are physically contracted, or that time slows down for you or that you increase your mass. Physically nothing changes by being observed to be moving at near light speed.

Considering the reference frame of a photon goes one step further and means that you cannot even make sense of things like a measurement of length. You don't physically change because there is EM radiation passing the Earth. It just means that you cannot be adequately described in a frame of reference moving at light speed.

This is why it's often best to describe something in its own rest frame. I.e. where it is not moving. This would apply to you, the Earth or a Black Hole. Then, you can transform those measurements to any valid frame of reference (that's everything except a reference frame moving at light speed). The measurements change, but the defining phyiscal characteristics do not change. You are still a person, the Earth is still a planet and a Black Hole is still a Black Hole.

The analogy is that a house remains a house whether you look at it from the front, the side or from above. A house doesn't become "just a roof" because that's all you can see of it.

 

[Herman Trivilino]

TL;DR Summary: Length contraction creates black hole around photon

Length contraction is derived from, and therefore applies only to, frames of reference. Frames of reference never travel at light speed, therefore length contraction is undefined for something travelling at light speed.

Also, if a particle travels past you at near light speed, it doesn't contract you and therefore can't turn you into a black hole.