Do we understand what the Universe looks like for a photon?

[fbs7]

The other day I was playing my favorite time waster (World of Warcraft), and someone started to talk about flat earthers. I thought of stirring world chat a little bit, so I posted that while the flat earthers were a lot of odd folks, one could argue that for a photon the Earth indeed looks flatter than a pancake - that got me a lot of insults and meltdowns, so it was a lot of fun with teenagers, but it got me thinking.

I really have no idea how the Earth or even the Universe looks like for a photon, but I suppose that photons still obey cause and effect, so that if we see a photon going on a line from "A" to "B" to all the way to the edge of the observable universe will, the photon will see everything in that line as a single point, yet somehow, by some bizarre mechanism, the effects of points "A", "B" and "edge of the universe" will affect the photon in that order - maybe because they are in the same 2D location but at different times?

I'm probably butchering physics with my poor language, but this idea that "A", "B" and "edge" show up in the same point kinda makes some little sense to my uneducated brain, as exactly the same thing happens in my 2D computer display. If I look at a set of coordinates in the display, that at 10:00 show the letter "A", then at 10:01 show "B", and show 10:02 show "C", then the coordinates of the letters A, B, C will all be the same, but I don't think they are on top of one another as they show at different times.

So, does it make any sense to compare that for a photon the whole universe looks like a 2D computer screen, where all the particles in the half of the universe that match the direction of travel (ie, the universe in the "front" of the photon) are arranged(**) in a fashion akin to the frames of a movie, while the other half of the universe (ie, in the "back" of the photon) is completely dark to the photon and will never be seen, given that nothing can catch up with the speed of light?

(**) I'm using the word "arranged" just for my complete ignorance of the proper term; a photon can't see anything, of course, and if it could see I'm not sure it could measure that in times as "10:00", "10:01" and so on; I mean with "arranged" the order that things affect the photon, ie, cause/effect - with my apologies up front for poor language.

 

[phinds]

Do we understand how the universe looks like for a photon?

There is no such thing. It is a common misconception that one can speak of "the point of view of a photon" but one cannot. There is a FAQ about that somewhere on this forum but I don't have a link at hand.

 

[PeterDonis]

There is a FAQ about that somewhere on this forum but I don't have a link at hand

It's here:

https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/
That FAQ is actually in the relativity forum, which is why I have just moved this thread to that forum.

 

[fbs7]

Oh, that's a mind-blowing idea! So if I understood it right it makes no sense to try and calculate a coordinate system from the reference of a photon, right? Wow!

That's amazing! So a photon has no size, right (otherwise it would have some coordinates to calculate the size), no internal structure (as that requires a size of some kind), has no time (another coordinate), no past, present and future (as these require time).

So can we say at all that a photon obeys causality? If it makes no sense to refer to time or past/present/future, then no point to refer to causality either?

Do we understand what's the internal nature of the photon, or is this an "we don't know yet" topic?

 

[Ibix]

So if I understood it right it makes no sense to try and calculate a coordinate system from the reference of a photon, right?

"Reference frame" and "coordinate system" mean the same thing in this context. It makes no sense to try to construct one in which light is at rest, which is usually what we mean by "from the perspective of".

So a photon has no size, right (otherwise it would have some coordinates to calculate the size),

That doesn't follow. We can still measure properties of photons. It's just that any sentence like "From the photon's perspective, its size/mass/colour/smell/whatever is..." makes no sense because you can't define its perspective, not because it doesn't have those properties. It probably doesn't smell though.

So can we say at all that a photon obeys causality?

Of course. Light interacts with matter, so if it could act non-causally then so could matter. Have you ever gone into a room at night and found it lit even though the light was off?

If it makes no sense to refer to time or past/present/future, then no point to refer to causality either?

These concepts make perfect sense for us observing a light pulse and light clearly does obey causality (radar is the obvious precise measurement where timing light travel is tested millions of times a day). It's just impossible to talk about the light's own view of itself, because attempts to do so end up being self contradictory. But that doesn't mean it doesn't have properties. Bad analogy warning: is a blind person invisible to everyone else because they can't see themself?

Do we understand what's the internal nature of the photon, or is this an "we don't know yet" topic?

My understanding is that photons are currently regarded as fundamental. We don't have any suspicions that there's anything "inside" them. So it's a bit stronger than "we don't know yet" - leaning towards a statement that there isn't anything to see.

Statements like that have changed in the past. But it's the current state of knowledge.

 

[hilbert2]

An object needs to be made of a very large number of elementary particles before it can interact with its environment in a complex enough way to tell what's going on around it. So things don't "look like" anything to a single particle like a photon. But it's true that in a reference frame moving at speed of light compared to any object with nonzero mass, the Lorentz contraction would make all distances zero in the direction of motion.

 

[PeterDonis]

in a reference frame moving at speed of light

There is no such thing. That's the point of the FAQ article I linked to in post #3.

the Lorentz contraction would make all distances zero in the direction of motion

No, this is not correct. The Lorentz transformation is singular for this case, so "Lorentz contraction" is not well-defined for this case.

 

[hilbert2]

No, this is not correct. The Lorentz transformation is singular for this case, so "Lorentz contraction" is not well-defined for this case.

I didn't mean that in the exact mathematical sense, more like "if the velocity to some direction is approaching speed of light, the Lorentz contracted distances in that direction will approach zero".

 

[PeterDonis]

more like "if the velocity to some direction is approaching speed of light, the Lorentz contracted distances in that direction will approach zero"

That's correct, but it has nothing to do with the properties of a photon. A photon is not a "limiting case" of Lorentz transformations of timelike objects at relative velocities approaching $c$. The action of Lorentz transformations on photons is discontinuous from its action on timelike objects: Lorentz transformations rotate timelike vectors but dilate null vectors. The latter is not a limiting case of the former.

 

[Ibix]

But it's true that in a reference frame moving at speed of light compared to any object with nonzero mass, the Lorentz contraction would make all distances zero in the direction of motion.

As Peter says, this isn't true. We can imagine accelerating a person (or just a camera) to 0.99999c compared to us, and use the Lorentz transforms to determine what the universe would look like for that person. But any attempt to describe what you would see if you pushed a camera to light speed fail on the self-contradiction given in the article Peter linked. This turns out not to matter because it's impossible to accelerate something to light speed. This is often phrased in terms of needing infinite energy, but the simplest reason is just that, at any time during the acceleration, your camera can measure the speed of light relative relative to itself and will always find it to be 3×10⁸m/s. So it always still has to increase its speed by that amount by its own measurements, so it can never get there.

Limiting cases are not applicable to this situation.

 

[hilbert2]

Ok, thanks for the clarifications.

 

[fbs7]

How about this.. instead of a photon, say that I speed up myself up to 0.99999999999c.

I understand I'd weight more than a trillion elephants in that case, but humor me. I think everything in front (meaning, in my direction of motion) would look very very red, and everything behind would look very very very blue. Now I'm passing by the Earth... would the Earth indeed look like a very flat pancake?

Then I get me a big telescope at my really-high-speed-spaceship. Then I look to my right (that is, perpendicular to the direction of motion), and if I could measure I'd measure the cosmic horizon (ie, limit of the observable universe) at some 13 billion light years away, just as it is for us... but if I measured that ahead, then I'd measure it at a much smaller distance, is that correct?

 

[Ibix]

I understand I'd weight more than a trillion elephants in that case, but humor me. I think everything in front (meaning, in my direction of motion) would look very very red, and everything behind would look very very very blue

Other way around - stuff you are moving towards will be blue (gamma rays, in fact) and very very bright, and stuff you are moving away from will be red and invisibly dim.

Now I'm passing by the Earth... would the Earth indeed look like a very

Actually, no, because it's moving almost at the speed of light - which makes it appear stretched out, more or less cancelling the contraction. If you measure the length with a ruler, however, this measures the locations of the leading and trailing limb of the Earth at the same time and it will measure as length-contracted, as expected.

 

[PeterDonis]

Actually, no, because it's moving almost at the speed of light - which makes it appear stretched out, more or less cancelling the contraction.

There will, however, be an apparent rotation:

https://en.wikipedia.org/wiki/Terrell_rotation

 

[phinds]

How about this.. instead of a photon, say that I speed up myself up to 0.99999999999c.

I understand I'd weight more than a trillion elephants in that case ...

No, you would weigh exactly what you weigh right now. You are using "relativistic mass", a concept that has been deprecated for about 90 years.

Think about it this way. You ARE moving at 0.99999999999c relative to a particle in the CERN accelerator. Do you feel any heavier?

 

[Nugatory]

How about this.. instead of a photon, say that I speed up myself up to 0.99999999999c.

Moving at 0.99999999999c relative to what? The launchpad your spaceship took off from, of course... but I could just as well say that that launchpad had started out moving in the other direction at 0.99999999999c and all my heroic acceleration has served only to slow me down so that I am now at rest.

 

[SiennaTheGr8]

... This turns out not to matter because it's impossible to accelerate something to light speed. This is often phrased in terms of needing infinite energy, but the simplest reason is just that, at any time during the acceleration, your camera can measure the speed of light relative relative to itself and will always find it to be 3×10⁸m/s. ...

I agree with this.

And if I'm not mistaken (someone please correct me if I am), the "infinite energy" explanation isn't just less simple—it's also incorrect. It takes this equation:

$E = \dfrac{mc^2}{\sqrt{1 - (v/c)^2}}$

(for $m > 0$) and says that setting $v=c$ yields $E = \infty$ (it's actually undefined). Perhaps I'm being pedantic, but I do think that it sometimes gives people the wrong idea ("If only we could harness enough energy," or "We'd need all the energy in the Universe").

 

[kimbyd]

How about this.. instead of a photon, say that I speed up myself up to 0.99999999999c.

I understand I'd weight more than a trillion elephants in that case, but humor me. I think everything in front (meaning, in my direction of motion) would look very very red, and everything behind would look very very very blue. Now I'm passing by the Earth... would the Earth indeed look like a very flat pancake?

Quibble: the concept of mass changing with velocity is an outdated concept. From your perspective, your mass is the same no matter what reference frame you are in. In modern terminology, relativistic momentum and energy are:
$$p = \gamma m v$$
$$E = \gamma m c^2$$

They used to replace $\gamma m$ in these equations with the concept of "relativistic mass", but this use fell out of fashion because it caused too many errors. Since from your perspective, $\gamma = 1$ for you always, you can never observe your own mass to increase due to relativistic effects even when using relativistic mass.

With that quibble aside, yes. When traveling at velocities close to the speed of light relative to your surroundings, those surroundings will appear flattened like a pancake along the direction of motion.

Specifically, the gamma factor at that speed (where $v = c(1-10^{-11})$) is roughly 224,000. This means that if you were traveling from Alpha Centauri to the Earth, the 4.3 light year distance would be shortened to a mere 10 light minutes. As you are traveling so close to the speed of light, you would cross that 10 light minute distance in ten minutes.

Then I get me a big telescope at my really-high-speed-spaceship. Then I look to my right (that is, perpendicular to the direction of motion), and if I could measure I'd measure the cosmic horizon (ie, limit of the observable universe) at some 13 billion light years away, just as it is for us... but if I measured that ahead, then I'd measure it at a much smaller distance, is that correct?

That's complicated. The CMB would be incredibly blueshifted in the direction of travel, so that it would be something like 1,200,000C in temperature. But because the distance to the CMB is inferred based upon a cosmological model, and not measured directly, it's not so easy to conclude that the distance to the CMB would be changed. It's easy to talk about length for local objects shortening due to relativsitic effects. But distances are a complicated topic in curved space-time.

 

[fbs7]

Oh... wow!... that's incredible discussion! I appreciate everybody jumping into help a bloke out with this stuff!

So my mass seems would be just like my regular mass to me - what a silly thing of me to think the opposite! After all, there's no preferred reference frame! Silly silly silly!

But now... hmm... now I'm with a hole in my head -- these things with relativity are fascinating! -- with this train of thought: I'm at Earth, and I look at all directions and everything seems to be going away from me at rates that seems independent of the direction I'm looking at (I guess after I compensate for the galaxy rotation and the Earth rotation) - due to the expansion of the universe thingie.

So the universe is, how you say... iso-something... that is, independent of direction.

Now I get in my spaceship, say "Mr Spock, Engage!", and launch myself into the void at constant speed 0.9999999999c relative to the center of the galaxy. But now I see the distant stars very much blue shifted in front of me, and red shifted behind me (not the opposite, hahaha! silly silly silly me!)

Isn't that a contradiction with the concept that there's no preferred uniformly moving frame of reference? Otherwise, I would just have to measure changes of redshift from distant stars to know which direction I'm moving in the universe?

 

[PeterDonis]

Isn't that a contradiction with the concept that there's no preferred uniformly moving frame of reference?

No, because "preferred" means "the laws of physics are not the same", not "the objects in the universe don't look the same". You are moving relative to the rest of the objects in the universe; that's why they look different to you than they would if you were at rest relative to them. But you still see the same laws of physics.

 

[kimbyd]

Yup. The universe is only isotropic and homogeneous to some observers. The important property is that there exists a class of observers for whom the universe appears homogeneous and isotropic. It is very possible to write down a universe where this is not the case (such as a rotating universe).