[jeffreyH (OP)]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

[chiralSPO]

What do you mean "at infinity"? If it had an infinite wavelength it would have zero energy. If it had traveled infinitely far, it would have the same energy it started with, unless we assume that it was getting red-shifted by spatial expansion the whole way, in which case it would have infinite wavelength, and zero energy.

[yor_on]

Are you thinking of limits? What then is a photons limit, it can't be its propagation (age). Or, if it is we don't see that limit astronomically, as we still see the 'first photons' reaching us from that Big Bang. I think Chiral might be hitting the hammer on the head there with red shift, and a accelerating expansion, though. Where does that 'energy' go?

[Ethos_]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

Thought provoking indeed.

From our frame of reference, the photon will red shift because of the expansion but take an infinity to be infinitely red shifted. However, because of time dilation, the photon will experience no passage of time between it's creation and that proposed infinity. From the photon's perspective, it will simply not have enough time to loose any energy.

I recognize that this view will probably not be met with much enthusiastic support but is nevertheless my opinion.

[Bill S]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

I keep thinking I must stop posting about infinity; then someone posts a gem like this!  []

I’m assuming the infinity you refer to is infinite wavelength.  You talk of “approaching infinity”, so you are starting with a finite wave.  Not only can something finite never become infinite, it cannot approach infinity.  However much it progresses, it is still infinitely far away.   So the answer must be “no, it can never lose all its energy”.

Things are never that simple though, are they?  If it is losing energy, and energy is quantized, does it reach a point where the last quantum of energy is lost?  If so, what happens to the wavelength?  Would there still be a photon?

If something is infinite, it must always have been infinite. (There’s a good example of how difficult it is to talk about infinity without using the terminology of the finite like “…always have been”.)  Could an eternal photon exist that had infinite wavelength?  As Chiral pointed out, with infinite wavelength it would have zero energy.  Is it a photon?

the photon will experience no passage of time between it's creation and that proposed infinity.

10/10 for bravery in stirring up that hornets’ nest.

[PmbPhy]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

I agree with chiralSPO in that photons will continually decrease in energy the further they travel. But I don't see it being exponential. Why "exponential"?

[jeffreyH (OP)]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

I agree with chiralSPO in that photons will continually decrease in energy the further they travel. But I don't see it being exponential. Why "exponential"?

I was looking for opinions on this and included the idea of an exponential decline to see what the reaction would be. I don't have that view myself. It was a bit provocative.

[jeffreyH (OP)]

The reason for posting this was the thought that a gravitational field extends to infinity. If the field removes energy from the photon at source and extends an infinite distance then there is an infinite opportunity for the field to carry on removing photon energy. Ultimately this would remove at least a large proportion of the energy, if not all of it. If it removes all the energy then this may mean that the wave nature of matter may depend upon the presence of gravity. An unusual concept I must admit. If it were true then gravitational waves are in evidence in the dual nature of the particle. Just my two cents worth.

[evan_au]

If [a photon] is losing energy, and energy is quantized, does it reach a point where the last quantum of energy is lost?   ...Would there still be a photon?

I think this might be confusing a light source emitting many photons with the behaviour of a single photon?

• Let's say a light source is emitting (say) a billion photons per second for an hour into space. A detector at Alpha Centauri would be very unlikely to detect one of these photons. From the viewpoint of a detector at the Andromeda galaxy, it (almost certainly) wouldn't see any photons from such a light source; from it's viewpoint, there wasn't a photon! This applies quantisation of light to a source emitting many particles.
  
• However, I understand the original post to be asking about the behaviour of a single photon. If you could follow one of the billions of photons, it would continue to propagate indefinitely through space until it impacts matter or a detector of some sort. If a local observer in a distant galaxy detected this photon, the energy of the photon would be lower than when it was emitted, due to cosmic redshift. I know of no lower limit to this photon energy, but it is still quantised as 1 photon, which still exists. (I guess in the extreme, if the photon wavelength was comparable to the size of the universe, then that is some sort of limit; but it would become undetectable by our equipment long before that!) 

[jeffreyH (OP)]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

Thought provoking indeed.

From our frame of reference, the photon will red shift because of the expansion but take an infinity to be infinitely red shifted. However, because of time dilation, the photon will experience no passage of time between it's creation and that proposed infinity. From the photon's perspective, it will simply not have enough time to loose any energy.

I recognize that this view will probably not be met with much enthusiastic support but is nevertheless my opinion.

The wavelength changes over time and so can we say the wave 'experiences' time? I doubt it.

[evan_au]

Oops! Crossed posts...

If the field removes energy from the photon at source and extends an infinite distance then there is an infinite opportunity for the field to carry on removing photon energy.

The scenario imagined here seems to be something like: a single Sun in the universe, and looking at the photon energy at large distances from the Sun.

If you follow one photon from the Sun, and measure the photon's energy in the Sun's frame of reference (no cosmic redshift), will the photon energy approach zero, due to Einstein redshift?

As I understand it, the answer is "No": although the Sun's gravitational field extends to "infinity", it decays as the square of distance, so the total effect on photon energy is "finite". The photon will lose only a tiny fraction of its energy as it travels to infinity*.

There is a critical mass & density where the Sun's gravitational field is so strong that the photon energy would become zero, and it does this in a finite distance - the Swarzchild radius of a black hole.

*This is similar to the concept of an "escape velocity" from the Solar System; although the Sun's gravitational field extends to infinity, it will subtract at most a finite amount of energy from a body moving away from the Sun. Using Newton's physics, Laplace deduced that black holes existed, because the escape velocity of a massive Sun would exceed the speed of light! Pretty impressive for someone who didn't know about Doppler Shift, Einstein Shift or relativistic time dilation!

[jeffreyH (OP)]

Oops! Crossed posts...

If the field removes energy from the photon at source and extends an infinite distance then there is an infinite opportunity for the field to carry on removing photon energy.

The scenario imagined here seems to be something like: a single Sun in the universe, and looking at the photon energy at large distances from the Sun.

If you follow one photon from the Sun, and measure the photon's energy in the Sun's frame of reference (no cosmic redshift), will the photon energy approach zero, due to Einstein redshift?

As I understand it, although the Sun's gravitational field extends to "infinity", it decays as the square of distance, so the total effect on photon energy is "finite"*.

There is a critical mass & density where the Sun's gravitational field is so strong that the photon energy would go to zero, and it does this in a finite distance - the Swarzchild radius of a black hole.

*This is similar to the concept of an "escape velocity" from the Solar System; although the Sun's gravitational field extends to infinity, it will subtract at most a finite amount of energy from a body moving away from the Sun. Using classical (Newton's) physics, Laplace showed that black holes existed, because the escape velocity of a massive Sun would exceed the speed of light! Pretty impressive for someone who didn't know about Doppler Shift, Einstein Shift or relativistic time dilation!

I do agree that the gravitational field should only remove a finite amount of energy even over an infinite distance. I was simply stating an alternative view. Black holes are a different matter.

[Ethos_]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

Thought provoking indeed.

From our frame of reference, the photon will red shift because of the expansion but take an infinity to be infinitely red shifted. However, because of time dilation, the photon will experience no passage of time between it's creation and that proposed infinity. From the photon's perspective, it will simply not have enough time to loose any energy.

I recognize that this view will probably not be met with much enthusiastic support but is nevertheless my opinion.

The wavelength changes over time and so can we say the wave 'experiences' time? I doubt it.

We see the wavelength change in our frame but does that mean it also changes in the photon's frame? I'm guessing it doesn't. The photon recognizes no passage of time.

[chiralSPO]

Is the red-shift an issue of wavelength increase over time, or over space? We can say that the longer (time) a photon travels, the more red-shifted it is, and we can say the farther (space) it travels, the more red-shifted it is. Both are true because c is a constant with units of m/s. But which of these determines the redshift?

What if, instead of a photon, we have an electron moving at 0.99 c? It has a wavelength too. If an electron and a photon are both emitted simultaneously from the same point source (bear with me here) and both arrive at a destination that was 100 ly away when they were emitted, the photon arrives first, and the electron about a year later. Was is the magnitude of the difference in their red-shifts?

[jeffreyH (OP)]

When approaching infinity would there be an exponential loss of photon energy? This is not a trivial question to answer in my view and should be thought provoking.

Thought provoking indeed.

From our frame of reference, the photon will red shift because of the expansion but take an infinity to be infinitely red shifted. However, because of time dilation, the photon will experience no passage of time between it's creation and that proposed infinity. From the photon's perspective, it will simply not have enough time to loose any energy.

I recognize that this view will probably not be met with much enthusiastic support but is nevertheless my opinion.

The wavelength changes over time and so can we say the wave 'experiences' time? I doubt it.

We see the wavelength change in our frame but does that mean it also changes in the photon's frame? I'm guessing it doesn't. The photon recognizes no passage of time.

That is a very interesting point. That suggests that the photon experiences no change in frequency. It would be the observer external to the photon's frame of reference that would see a change in frequency.

[chiralSPO]

I don't think photons can "observe" space either...

[PmbPhy]

I don't think photons can "observe" space either...

Correct. A lot of confusion arises when people start talking about the experiences of photons.

[jeffreyH (OP)]

Experience is a very bad choice of word. Not very scientific really.

[JohnDuffield]

The reason for posting this was the thought that a gravitational field extends to infinity. If the field removes energy from the photon...

It doesn't. The ascending photon doesn't lose any energy. In similar vein the descending photon doesn't gain any energy. If you send a 511keV photon into a black hole, the black hole mass increases by 511kev/c². Conservation of energy applies. The descending photon appears to be blueshifted because you and your clocks go slower when you're lower.

[Ethos_]

Experience is a very bad choice of word. Not very scientific really.

Very true if we are only considering the photon as observer. However, if it were possible for one of us to travel with the photon, which we all know it is not, we could experience or observe the photon's frame and frequency. Because that is not possible, we can only surmise. And to be clear, my opinion about this subject is only that, an opinion.