Connected events at opposite ends of a photon's travel

[KenJackson]

Someone started a recent thread with a statement that included "light exists outside of time". That excerpt was flatly rejected, and the post generated such a lively response that it was closed, having "wandered off into philosophy".

It made me wonder if "light exists outside of time" describes the thought I've had for some time.

Suppose, on a planet around a star a billion light years away, some event in an atom results in a photon traveling toward Earth. Much later, the photon strikes an atom on Earth causing an event witch absorbs the photon's energy.

Now both Earth and the remote planet have experienced about a billion years as the photon made its way from one to the other. But the photon itself did not experience any time at all (right?).

So can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

 

[Stephanus]

Dear Ken, perhaps I can help you.

...Now both Earth and the remote planet have experienced about a billion years as the photon made its way from one to the other.

Yes, I think so. Considering both Earth and the remote planet are comoving. That they are in the same frame. But it might not be that way because the Earth revolves around the sun about ...108 thousands km/hour or 30km/sec. I don't know about the orbital speed of the planet. But providing the planet has the same distance as the Earth's to the sun, we can say that for all practical purpose they are both comoving in relativity point of view.
Because their speed is negligible in relativity point of view.

But the photon itself did not experience any time at all (right?).

I think so. Because time stops for every object that moves at c. Object that moves at c will not experience time. Come on, even the great Albert Einstein wondered how the universe would look like if he rode in a photon.
And one more thing that I learn in PF.
Because of this velocity addition formula. $w = \frac{u+v}{1+uv}$, so every objects that moves at c wrt to something always moves at c wrt everything.

So can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

You can say that. "The events on both planets happened together wrt, with respect to the photon.
NOW has no significant meaning in relativity.

 

[Vitro]

... But the photon itself did not experience any time at all (right?).

So can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

The short answer is: there is no such thing as "photon's point of view" or "experience". There are many discussions around detailing why that is, but I can't think of specific ones to link here.

There's a one paragraph answer in the FAQ: https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170. Rest frame of a photon and photon's point of view are equivalent concepts.

 

[Stephanus]

Rest frame of a photon and photon's point of view are equivalent concepts.

Thanks Vitro for the answer (although it's not for me.) So the rest frame of an object is the object point of view? Is this the term in SR?
And I knew that photon has no rest frame, but I didn't know that photon does not have point of view.
It means that we can't draw photon worldline horizontally in Minkowski diagram. at least mathematically?

 

[Ibix]

@Stephanus - you are always "here" from your own point of view. So your point of view is a frame in which you are at rest - always at the same place with the world moving around you. But light cannot have a rest frame (if it's not accelerating then any such frame would be inertial - so light would have to move at 3x10⁸m/s and be at rest at the same time) so it cannot have a point of view.

 

[robphy]

So can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

Given a light ray from event A to event B,
B is to the future of A. That is, A happens then B happens. They are distinct events.

 

[KenJackson]

@Stephanus... (... - so light would have to move at 3x10⁸m/s and be at rest at the same time) ...

We seem to have a singularity, or at least a conundrum. Many things in math that don't make sense can be solved by taking the limit as something approaches something. So let's replace the photon with an unknown particle traveling a tiny bit slower than light.

It has a point of view and it experienced much less than a billion years during its trip. Now take the limit as its speed approaches the speed of light. Doesn't the limit of the time experienced approach zero?

 

[Mister T]

Now both Earth and the remote planet have experienced about a billion years as the photon made its way from one to the other. But the photon itself did not experience any time at all (right?).

Loosely speaking, photons do not experience time. But let's formulate the situation in a way that allows us to speak rigorously. Let's say Earth and the remote planet are indeed $10^9$ light years apart and are at rest relative to each other. A particle travels from the planet to Earth so fast that it experiences one second of time. So, a billion years will have elapsed for people on Earth, but only one second of time will have elapsed for the particle. If it was, for example, a particle that lives for only two seconds in its own rest frame, it will indeed live to make the journey.

 

[Mister T]

It has a point of view and it experienced much less than a billion years during its trip. Now take the limit as its speed approaches the speed of light. Doesn't the limit of the time experienced approach zero?

For the particle, yes. For people on Earth, no.

 

[KenJackson]

A particle travels from the planet to Earth so fast that it experiences one second of time. So, a billion years will have elapsed for people on Earth, but only one second of time will have elapsed for the particle.

(Wow. You and I posted a similar theme at about the same instant from our distance. That seems to be coincidental cubed--timing, theme, and vaguely illustrative.)

You seem to confirm my thought. I'm still trying to connect the two events on the two planets that happened a billion years apart as observed from either planet. They seem to me to have happened at the same instant with respect to light and are therefore two parts of one event.

I'm not sure what significance this has, but its utterly fascinating.

 

[Ibix]

We seem to have a singularity, or at least a conundrum. Many things in math that don't make sense can be solved by taking the limit as something approaches something. So let's replace the photon with an unknown particle traveling a tiny bit slower than light.

It has a point of view and it experienced much less than a billion years during its trip. Now take the limit as its speed approaches the speed of light. Doesn't the limit of the time experienced approach zero?

You can make the time the particle experiences in the crossing arbitrarily small by making the particle move arbitrarily close to the speed of light, yes. However, to the particle, it is at rest and your clocks are running slow. The reason for the short duration of the crossing (actually, the stars are moving in this frame, not the particle, so crossing isn't quite the right word) is that the distance between the planets is length contracted.

Try to carry this reasoning on to something traveling at light speed, though, and you run into nothing but contradictions. If you want to say it experiences no time then, in its experience, you experience no time because you are moving at light speed relative to it. Yet your clocks advance. If you want to say that it experiences no time between emission and reception because the distance between the two events is zero, it can say the same about you. Yet your rulers make useful measurements. If everything is length contracted to the same place, what would you mean by "first" in the phrase "the photon is absorbed by the first thing it strikes"?

There isn't a coherent way to describe a photon's "point of view". It's a contradiction even talking about it, for the reason I gave Stephanus. Mathematically, the problem is that you are assigning the same coordinate to multiple events in spacetime and hoping to reason from there. It's kind of like asserting that all points on the surface of the Earth lie on the equator and hoping you will be able to navigate anyway.

 

[Laurie K]

I'm still trying to connect the two events on the two planets that happened a billion years apart as observed from either planet. They seem to me to have happened at the same instant with respect to light and are therefore two parts of one event.

KenJackson, I can remember reading recently that cosmological red shift occurs between a photons emission point and its subsequent absorption point.

If the emission point continues to emit photons during the photons traveling time and the emitted 'in transit' photons are not blocked or distorted along the way then there should exist a continuous stream of discrete photons between the source and the observer at the time of the observation i.e. now, unless you regard the entire photon stream as one photon (a billion light year long quanta of light?).

 

[ExecNight]

When the photon leaves the planet, it actually instantaneously strikes the Earth therefore the event is completed. But, it takes one billion years for the universe to process this information. And therefore we can not observe something when the information about the event has not reached us yet.

Although this sounds very ridiculous, this is actually what time dilation equation says in my understanding. When v = c, t becomes indefinite is pretty much what the above can be interpreted as, don't you think?

*Ducks*

 

[Ibix]

When v=c you are violating the assumptions upon which the time dilation equation rests. You can put v=c into it, but the answer is meaningless.

 

[Mister T]

When the photon leaves the planet, it actually instantaneously strikes the Earth [...]

No, it doesn't. The amount of time that elapses between the two events depends on the frame of reference in which that time is measured. There is no frame of reference in which that elapsed time is zero.

therefore the event is completed.

An event has no extension is space and no duration in time. It therefore makes no sense to say that an event is completed or not completed. It's simply an assignment of spacetime coordinates.

But, it takes one billion years for the universe to process this information.

That's true in one frame of reference, but not true in many many others.

 

[ExecNight]

No, it doesn't. The amount of time that elapses between the two events depends on the frame of reference in which that time is measured. There is no frame of reference in which that elapsed time is zero.

Well, we don't know that because like it was said here, current equations doesn't give an answer to the situation. But we also know there are two frames in the universe that move wrt each other faster than c, galaxies far enough experience this because of the expansion of space. So, this is actually a natural thing that happens. Yet, not modeled how.

An event has no extension is space and no duration in time. It therefore makes no sense to say that an event is completed or not completed. It's simply an assignment of spacetime coordinates.

Like i said, this is unknown since current equations explaining this phenomenon are not answering the situation.

That's true in one frame of reference, but not true in many many others.

Exactly, actually we should be able to experience this phenomenon. If we can launch a telescope into our solar system and accelerate it to say 100.000 km/s. Our observable universe, should differ from its observable universe. Wish i had a few billion dollars to try this out.

 

[m4r35n357]

Like i said, this is unknown since current equations explaining this phenomenon are not answering the situation.

This is not an equation, it is a definition, and you don't get to challenge it ;)

As for your "instantaneous" light pulse, what you have done is calculated the spacetime interval, then interpreted it as if it were a (time) coordinate interval. Schoolboy error.

 

[Nugatory]

But we also know there are two frames in the universe that move wrt each other faster than c, galaxies far enough experience this because of the expansion of space. So, this is actually a natural thing that happens. Yet, not modeled how.

This situation is completely and correctly modeled by general relativity. Although the recession velocity of two sufficiently distant galaxies will exceed $c$, this recession velocity is not a speed in the sense that you're trying to use it - you can't multiply it by a time to get a distance traveled and it has nothing to do with the $v$ that appears in the time dilation and length contraction equations of special relativity. You certainly cannot use it to define two inertial reference frames that are moving at speeds greater than $c$ relative to one another.

 

[PeterDonis]

both Earth and the remote planet have experienced about a billion years as the photon made its way from one to the other.

Only if you assume a certain simultaneity convention. That is, you have to pick some event on Earth that is simultaneous with the event of the remote planet emitting the photon; and you have to pick some event on the remote planet that is simultaneous with the event of the Earth receiving the photon. Only if you make certain choices for both of those things will the statement quoted above be true. And it is easy to make alternate choices for those things that make that statement false.

What this is really telling you is that the statement quoted above is not a statement about physics; it's a statement about human conventions. So you have to be very careful trying to draw physical inferences from it.

can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

No, because there wasn't only one event, there were two. And there were also an infinite number of events in between them, all on the photon's worldline. The fact that the "arc length" of the photon's worldline is zero does not mean there are no events on it. It just means those events are not distinguished by arc length; they are distinguished by some other parameter.

Doesn't the limit of the time experienced approach zero?

Yes, but that doesn't mean what you appear to think it means. See above.

 

[KenJackson]

That is, you have to pick some event on Earth that is simultaneous with the event of the remote planet emitting the photon; and you have to pick some event on the remote planet that is simultaneous with the event of the Earth receiving the photon.

The intention was that the cause and timing of the event on the remote planet are unknown and unimportant--only that it resulted in a photon being emitted.

And the event on Earth would be caused when the photon struck an atom, that is, the photon caused the event, so it wouldn't be picked.

Also, I didn't state it, but I assumed the planets would be moving much, much slower than the speed of light with respect to each other.

I suspect all the points have been touched on this one.

 

[Dale]

So can we say that from the photon's point of view, the events on both planets happened together and are connected, as if there was really only one event?

No, we cannot say that. A point of view is a reference frame (or coordinate chart), and a photon does not have a valid reference frame. So the phrase "photon's point of view" is self contradictory.

The events on a photons worldline are distinct events. They are not simultaneous in any inertial frame. They cannot be parameterized by proper time but they can be parameterized by any other affine parameter.

 

[PeterDonis]

The intention was that the cause and timing of the event on the remote planet are unknown and unimportant

If so, then there is no basis for your statement that a billion years passed on the remote planet between the photon being emitted there and the photon being received on Earth. Which was the statement I was questioning. So my criticism is valid if this was your intention.

the event on Earth would be caused when the photon struck an atom, that is, the photon caused the event, so it wouldn't be picked.

Read what I said again, carefully. I did not say the event of the photon being received on Earth would be picked.

I didn't state it, but I assumed the planets would be moving much, much slower than the speed of light with respect to each other.

In a curved spacetime, there is no well-defined "relative velocity" between objects that are spatially separated. So this assumption is not valid for your scenario, since it requires the relative velocity of the Earth and the remote planet to be well-defined.

 

[KenJackson]

If so, then there is no basis for your statement that a billion years passed on the remote planet between the photon being emitted there and the photon being received on Earth. Which was the statement I was questioning. So my criticism is valid if this was your intention.

You're attacking the problem setup, not the conclusion. I said the planets experienced "about" a billion years as the photon traveled a billion light years because I wanted to avoid quibbles over difference due to small relative velocities. Those differences aren't what I was asking about.

 

[PeterDonis]

You're attacking the problem setup, not the conclusion.

If the problem setup is flawed, would you expect the conclusion to be valid?

I said the planets experienced "about" a billion years as the photon traveled a billion light years

Then you still haven't fixed the issue I posed. You can find simultaneity conventions in which neither planet experiences "about" a billion years--in fact, you can find simultaneity conventions in which both planets' experienced time between photon emission and reception is arbitrarily close to zero. So in order to state that they experience "about" a billion years, you still have to restrict yourself to a very small subset of all the possible simultaneity conventions, even if you are not technically singling out one unique one.

 

[Mister T]

Well, we don't know that because like it was said here, current equations doesn't give an answer to the situation.

You've misunderstood what was said in that regard. We do know, as well as we know anything else we've said, that it's not possible for a frame of reference to move at speed c.