[Karl McKillop]

Karl McKillop asked the Naked Scientists:
   
Concerning the red shift of different objects in the cosmos.

If each photon's wavelength is shifted to the red then the energy of that photon is decreased as the energy of a photon is inversely proportional to its wavelength.

So where has this lost energy gone? Is this the explanation of Dark Energy?

Perhaps the energy of a photon is not fixed but does decay even though it is only appreciable over cosmic scale distances and time?

What do you think?

[graham.d]

If you are thinking of the redshift that is observed from distant galaxies this is thought to be due to the Hubble expansion of the universe. The simple explanation for this is that more distant galaxies are moving away faster than nearer ones and so have a greater redshift; this being due to Doppler effect. In the same way that sound from a receding train is lower frequency, so is light emitted from stars that are receding from us. It is not thought, at least conventionally, that the photon is losing energy as it moves.

[Bored chemist]

However it happens that the photon's wavelength is shifted to the red it still means that the photon has less energy than it had when it set out.
The question "where did the energy go?" is a valid question.

[Farsight]

I think this:

The redshifted photons haven't actually lost any energy, and instead it's an observer effect. For example if you measure the frequency of light coming from a source, and then move away from that source and measure the frequency again, you'll measure it to be redshifted, but you don't wonder where the energy has gone. The redshifted CMBR associated with the expansion of the universe is something like this, but is a "scale change". IMHO it can be likened to gravitational redshift. When you're down near a planet you're subject to gravitational time dilation. If you measure the frequency of light shining up into space, and somebody up in space measures it too, they measure a lower frequency. You might then say it had lost energy, but this overlooks gravitational time dilation, which means you're using different time-scales to measure the frequency.

[graham.d]

OK, BC, I guess that is not obvious from my answer which I thought was referring to energy loss en route. From the perspective of the emitter the photon has a certain frequency and wavelength meaning a specific energy. But from our perspective, as we are moving apart from the emitter, the energy we see in the photon is less. For photons this lower energy is a longer wavelength and is analogous to the longer wavelength sound we hear from a receding train, which also has lower energy. From a particle viewpoint if I throw a cricket ball to you you will absorb the energy as you catch it. If I throw a cricket ball to you, just as hard from my perspective, but from the back of a vehicle moving away from you it will reach you with a slower speed and lower energy.

Whilst both the sound analogy and the cricket ball analogy are valid in showing the lower energy as a result of the source receding from us, light is a little more complicated because it is neither a wave travelling in a fixed medium like air (or an aether) nor a solid object, or particle in a similar sense to a ball. However, for considerations of where the energy goes it is similar.

The energy to cause the emission comes from the emitter. For a photon this may be an electron moving to a lower energy state in an atom for example. If we look at the cricket ball we can assume that the energy of my throw is the same in every case, but if we take the case where the vehicle is moving away from you at close to the speed of my throw, to you it will simply drop down on the road with no velocity at all. To you the ball has no kinetic energy. The Kinetic Energy of an object depends on its speed relative to you.

In both cases energy is conserved but you have to look at the total energy of the emitter + photon (or thrower plus vehicle plus ball) before and after. This total energy and total momentum remains the same whether you do the calculation in Newtonian mechanics or with Special Relativity. The energy does not disappear. From the perspective of the observer (or catcher) the missing energy is in the slight increase in speed of the emitter (or thrower + vehicle).

Do you want the maths too?   :-)

[wolfekeeper]

Even in Newtonian mechanics, energy is a frame-dependent thing, not a property of the particle itself.

For example, if a car drives past you then it has 0.5 m v^2 kinetic energy relative to you. But if you're sitting in the car, it has no kinetic energy relative to you.

Frequency is also frame/situation dependent; when you hear an ambulance go past, its pitch changes, but if you were riding on the ambulance, then it would be constant.

Basically you're assuming something that obviously isn't true, that the energy of a photon is stored inside the photon. That's an incorrect assumption in relativity theory as well as Newtonian mechanics.

[Andrew P]

The energy really is lost, and in a more profound sense than energy is lost in normal 'doppler' shift or frame switching situations.

That's because the CMB radiation is arriving from every direction, so while you can change your speed to see a greater energy coming from one direction, that'll be compensated by a lower energy from the opposite direction (exactly cancelling at non-relativistic speeds).

So, actually, there is a preferred frame of reference in which the CMB looks the same in all directions, and in that frame the photons are slowly losing energy.

This is a reflection of the fact that, in general relativity, energy is not conserved. A more general quantity known as the 'energy-momentum tensor' is conserved instead. I gave a brief discussion of why this should be in the QA of a recent naked astronomy podcast... I think it was the February one...

To go back to the original question, this doesn't account for 'dark energy', which is a separate effect. The conservation (or non-conservation!) of mass and energy is consistently taken into account when calculating the evolution of the universe, and we still need dark energy to match the real observations.

Monthly astronomy podcasts - www.thenakedscientists.com/astronomy [nofollow]

[graham.d]

Andrew and the quote from Tommya are quite right about the effects of gravitational time dilation affecting the energy of a photon. There are a number of recent threads discussing this. Whether this is the dominant process in redshift of light from distant objects is debatable and it would be contraversial to suggest that, for example, the Hubble redshift is not mostly due to expansion. I am unsure how much this debate is informative to Karl.

The problem in discussing some of these subjects is that there are many ideas and very few experimental confirmations. Cosmology is like that. What is a fairly simple question can end up with an answer (a correct answer to most physics questions) that nobody knows. This is not very helpful, however, and disregards what is understood reasonably well, even if not wholly. To give a full answer would be a very long answer indeed, probably several books, and a full understanding would need deep knowledge of advanced mathematics.

But hey, this is a scientific website so let's go for it :-)

Andrew, is the preferred frame of reference you refer to just one that removes our local motion from observation of the CMBR? Isn't it to be expected that an expanding universe would result in the CMBR losing energy? After all they started off very hot and are now rather cold. Or are you speaking of a new phenomenon?

[Andrew P]

...it would be contraversial to suggest that, for example, the Hubble redshift is not mostly due to expansion.

The problem in discussing some of these subjects is that there are many ideas and very few experimental confirmations. Cosmology is like that.

Ah... now we're opening a can of worms! Yes, yes, my first post was slightly one-sided, but for a good reason which I'll try to explain. For those not interested in the minutiae, there are a couple of more down-to-earth points at the end...

Broadly, Graham, I agree with your points, but with a slight nuance. I don't think (in this context) the problem is that there are lots of ideas floating around which we are struggling to experimentally confirm. Instead, I'd say that -- in terms of the experimental tests -- one's view on 'whether redshift is an effect equivalent to doppler shift or not' is irrelevant. That's because the predictions for experiments, if done correctly, are totally independent of the interpretation, so long as you are consistent in how you apply the equations.

In fact I'd say it's not just cosmology -- all of physics is a bit like this. Abstract ideas like 'energy' or even 'redshift' can often be interpreted in different ways, so you just need to pick your favoured interpretation and make sure you understand its limitations.

When you go beyond these limits, you end up with apparent disagreements which largely come down to semantics. I find the long debates over 'is redshift due to expansion or due to relative velocities' (and you can find these debates in shady corners of the cosmology literature)  slightly ridiculous for exactly this reason.

Nonetheless, I stick my feet pretty much on one side of the fence: I go with the 'genuine energy loss' interpretation because I find that it's most useful for physical intuition. I argued this point in my first post. But I also agree there are certain circumstances under which you can usefully reinterpret what's going on as a frame-dependent effect.

Andrew, is the preferred frame of reference you refer to just one that removes our local motion from observation of the CMBR?

Yes, the preferred frame is exactly the one which makes us 'motionless' relative to the CMBR. That frame is defined by the 'isotropy' of the CMBR, in fact, because there's no other way to experimentally define it.

Isn't it to be expected that an expanding universe would result in the CMBR losing energy?

I guess whether you 'expect' it or not depends on how good your physical intuition is. If you expect it, that's good intuition!

After all they started off very hot and are now rather cold. Or are you speaking of a new phenomenon?

The idea that they've cooled down is very similar to the idea they have lost energy. The real puzzle, for most people, is 'where has that energy gone?'. The answer is that it hasn't gone anywhere because energy isn't conserved in GR (see my post above).

Monthly astronomy podcasts - www.thenakedscientists.com/astronomy [nofollow]

[graham.d]

Andrew, my intuition here was simply that the CMBR temperature fits with blackbody radiation assuming an expanding universe resulting in adiabatic cooling. I guess you are saying that the cooling is greater than this mechanism could predict (is that right?) so maybe this could be a result of the newly discovered accelerated expansion (??). If so then you can't discount the effects of dark energy, though not affecting the CMBR directly, but being possibly the ultimate cause of greater cooling than expected.

Indeed, GR would have conservation of energy-momentum but energy can also said to be conserved. I think, rather as you observe in your post, this is a matter of interpretation. In flat (Minkowski space) energy is conserved. It could be argued that the FLRW metric this is not a bad approximation though has a few issues with boundary conditions. Even then it could be said the energy is transformed into gravitational rather than not conserved. If you think of light emerging from a gravity well, the energy put in is in a different frame from when it is received. Observers in both frames will only agree on the total energy used if the gravitational effects are taken into account, including time dilation, and I don't think there will energy lost; it just depends on the frame. At least I think so.

To follow a discussion in another thread, do you know the formula for gravitational redshift from inside a massive sphere. i.e. that uses Gravitational potential as a function of radius. All the references I can find consider redshift outwards from the outside of a sphere and use field. It seems a lot of people make the mistake of then assuming the redshift is due to the field and then use the wrong maths.

[Andrew P]

Andrew, my intuition here was simply that the CMBR temperature fits with blackbody radiation assuming an expanding universe resulting in adiabatic cooling. I guess you are saying that the cooling is greater than this mechanism could predict (is that right?) so maybe this could be a result of the newly discovered accelerated expansion (??).

The rate of cooling exactly agrees with the prediction you'd make from adiabatic expansion. The difference is that adiabatic cooling refers to the situation where you have a load of particles in a sealed box with a movable piston and allow that piston to move slowly. In such a case, the loss of energy of the particles is compensated by the kinetic energy delivered to the piston. In other words, the energy is transferred outside the system of particles, but is conserved overall.

In the case of the Universe, there is no external system to transfer the energy to, so you come back to the question: where did the energy go? (With the same answer as ever: nowhere.)

If so then you can't discount the effects of dark energy, though not affecting the CMBR directly, but being possibly the ultimate cause of greater cooling than expected.

Dark energy does indeed affect the cooling rate indirectly, since it accelerates the expansion.

(Incidentally there is also a second, smaller, more subtle effect of dark energy on the CMBR. This is called the integrated sachs-wolfe (ISW) effect, as alluded to by tommya in the post above. This ISW effect wouldn't exist in an exactly uniformly spread-out (homogeneous) universe, whereas the other effects do.)

Indeed, GR would have conservation of energy-momentum but energy can also said to be conserved. I think, rather as you observe in your post, this is a matter of interpretation. In flat (Minkowski space) energy is conserved. It could be argued that the FLRW metric this is not a bad approximation though has a few issues with boundary conditions.

In a global sense the FLRW metric is very different from Minkowski space, and it is exactly this difference that means energy conservation goes out the window. (Specifically, it is the lack of time symmetry of the FLRW metric.)

Even then it could be said the energy is transformed into gravitational rather than not conserved. If you think of light emerging from a gravity well, the energy put in is in a different frame from when it is received. Observers in both frames will only agree on the total energy used if the gravitational effects are taken into account, including time dilation, and I don't think there will energy lost; it just depends on the frame. At least I think so.

You're right about this particular case, but it is just one case.

If you attempt to follow this into a formal definition of 'what is conserved in every situation', you'll end up with exactly the energy-momentum tensor. In many simple situations, that could be translated back into the language of gravitational potential energies -- but not always.

To follow a discussion in another thread, do you know the formula for gravitational redshift from inside a massive sphere. i.e. that uses Gravitational potential as a function of radius. All the references I can find consider redshift outwards from the outside of a sphere and use field.

In the case of weak-field gravity where matter is moving at non-relativistic speeds (like on, inside or around the Earth or Sun, for instance), you can always use the Newtonian potential without worry. In that case you'll find the gravitational redshift is always equal to ΔΦ/c^2 where ΔΦ is the difference in Newtonian potential between emitter and observer and c is the speed of light. Rather neatly, this result arises directly from the equivalence principle without even needing to go via GR itself!

The cosmological redshift effect can indeed be thought of consistently in this kind of way, as 'the photon continually climbing out of a gravitational field'. But in that case, the Newtonian expression doesn't work directly (the weak-field limit doesn't apply globally).

Monthly astronomy podcasts - www.thenakedscientists.com/astronomy [nofollow]

[Farsight]

Andrew and the quote from Tommya are quite right about the effects of gravitational time dilation affecting the energy of a photon.

I dispute this. I know it's what everybody says, but conservation of energy applies. If a gravitating body emits a photon with a given energy, that's how much energy the body loses. This energy is then lost to the system when the photon escapes. There is no actual mechanism by which some of the photon energy is transferred from the photon to the gravitational field or the body.

Take this to the limit where the gravitating body consists of two zillion electrons and positrons annihilating cleanly to produce 511keV photon pairs, all of which escape. Eventually there no body left, and no gravitational field either. All the energy has gone, and it all escaped as two zillion 511keV photons. 

[graham.d]

You raise a lot of points, Andrew. Thanks for your comments. I understand the need to do external work for adiabatic expansion of an ideal gas but this is not exactly the same as the universe though sometimes a convenient model. Could this not be effectively synthesised by the pressure reduction of matter condensing out? The energy is not lost in this case though it may appear so from just looking at em radiation in isolation.

I didn't understand why time assymmetry affects energy conservation or even why the FLRW metric results in this. Is this something to do with gravitational collapse? Can you explain or give a reference?

Can you give a clear example of energy conservation failure but where energy-momentum is conserved.

[Farsight]

...The cosmological redshift effect can indeed be thought of consistently in this kind of way, as 'the photon continually climbing out of a gravitational field'...

Nobody ever seems to talk about this. If you took our universe and removed everything bar the CMBR and the space it's moving through, you're left with a fairly uniform photon+spatial energy distribution and thus no gravity. If you make it smaller there's still no gravity, but the energy density is higher. This is rather like a void at the centre of the earth where the gravitational potential is flat but the time dilation is at a maximum - the coordinate speed of light is less than up in space, but you can't measure any difference locally. In similar vein the early universe would have been time-dilated, with a speed of light that's less than it is now. Again you can't measure this directly, but an observer would have seen the CMBR photons at a higher frequency than he sees them now. IMHO this maintains energy conservation for those CMBR photons.   

[Andrew P]

I understand the need to do external work for adiabatic expansion of an ideal gas but this is not exactly the same as the universe though sometimes a convenient model. Could this not be effectively synthesised by the pressure reduction of matter condensing out? The energy is not lost in this case though it may appear so from just looking at em radiation in isolation.

I'm not 100% sure I follow this. Are you talking about some sort of phase transition? It's not immediately clear to me that the Universe's expansion can be interpreted as an ongoing phase transition (and I've certainly not heard of anyone thinking of it in these terms), but I'd have to think about it.

I didn't understand why time assymmetry affects energy conservation or even why the FLRW metric results in this. Is this something to do with gravitational collapse? Can you explain or give a reference?

This relates to a deep but quite tricky idea in physics, that symmetry implies conservation, known as Noether's theorem. You can find a somewhat technical description at http://en.wikipedia.org/wiki/Noether%27s_theorem [nofollow].

I also tried to give a plausible argument for why this should be so in February's astronomy podcast, so you could see how convincing you find that

Can you give a clear example of energy conservation failure but where energy-momentum is conserved.

It's a little tricky to find very clear examples. The radiation content of the Universe would normally be regarded as one clear example, but given all the considerations above I can see it's not a great place to start in convincing you.

Dark energy is almost clearer, oddly, as follows. Even though the Universe is expanding, so you'd expect things to be 'thinning out', the physical density of dark energy stays the same. In this case, energy is not conserved. However, energy-momentum certainly is.

I'll have a think to see if I can come up with any other compelling examples, maybe use it in a future podcast.

... IMHO this maintains energy conservation for those CMBR photons.   

As I stated in one of my earlier posts the conclusion you come to will depend to a large extent on how you choose to define 'energy' in a context where it's pushed beyond its normal bounds of usefulness.

So: it doesn't conserve energy in the sense that if you measure the total usable energy of a fixed number of CMBR photons at an early time, then again at a later time, the energy won't be the same.

But if you like to attribute that to a time-dependent 'potential energy', I suspect you can (with care) get a consistent description of redshift effects from these considerations. You're right that people don't often state it in these terms, and I suspect the reason is that it's because it's actually harder than thinking about it in the more standard way!

The reason we turn away from fixing up normal energy conservation using potentials (ala Newtonian mechanics) to the more general notion of energy-momentum conservation is because the latter is much more generally applicable (see for instance the dark energy example just above).

[graham.d]

I understand the need to do external work for adiabatic expansion of an ideal gas but this is not exactly the same as the universe though sometimes a convenient model. Could this not be effectively synthesised by the pressure reduction of matter condensing out? The energy is not lost in this case though it may appear so from just looking at em radiation in isolation.

I'm not 100% sure I follow this. Are you talking about some sort of phase transition? It's not immediately clear to me that the Universe's expansion can be interpreted as an ongoing phase transition (and I've certainly not heard of anyone thinking of it in these terms), but I'd have to think about it.

I would not blame you for not following this. It was just a random thought. I suppose a sort of gradual phase transition; what started off as a sea of hot particles is not just ending as a sea of colder particles but some very large masses occupying a much smaller volume. Certainly the composition has changed. Wouldn't this behave like the external piston?

Yes, I can see that the theory about Dark Energy conserves the Energy-Momentum and not energy but I am a little skeptical about the whole concept of the expanding universe creating or (more like) uncovering more space. Candidates for the fundamental nature of Dark Energy are somewhat elusive with somewhat arbitrary fudges being applied to fit in with zero point energy from quantum theory. I will look up the reference when time allows. Regrettably I have to work in the less interesting field of semiconductors, but at least I do get paid for this.

[graham.d]

I should also say that phase transitions are not so unreasonable. The commencement of the so called "inflationary epoch" was due to a phase transition. Of course this is also the period of the creation of dark energy which causes the rapid expansion. So if we accept that there was an inflationary epoch, which seems necessary to explain the horizon problem, then we ahve to accept the creation of Dark Energy (I think), or at least something with similar properties. So I suppose the idea of the negative pressure and dark energy does hang together. It would be nice to understand the nature of dark energy so as to relate it to something testable - but I guess this is an outstanding problem that quite a few people are trying to solve.

[Farsight]

As I stated in one of my earlier posts the conclusion you come to will depend to a large extent on how you choose to define 'energy' in a context where it's pushed beyond its normal bounds of usefulness.

I feel it's something more than defining energy, but getting to the bottom of what energy actually is. And it's a tricky area... 

So: it doesn't conserve energy in the sense that if you measure the total usable energy of a fixed number of CMBR photons at an early time, then again at a later time, the energy won't be the same.

Usable energy is a case in point. When we consider the "heat death of the universe" there's no usable energy because the energy density is now uniform. But the energy itself has not been destroyed, just as it is not destroyed by an engine.   

But if you like to attribute that to a time-dependent 'potential energy', I suspect you can (with care) get a consistent description of redshift effects from these considerations. You're right that people don't often state it in these terms, and I suspect the reason is that it's because it's actually harder than thinking about it in the more standard way!

I'm not keen on potential energy myself, but going into the details would take us even further off-topic.

The reason we turn away from fixing up normal energy conservation using potentials (ala Newtonian mechanics) to the more general notion of energy-momentum conservation is because the latter is much more generally applicable (see for instance the dark energy example just above).

Noted Andrew. I confess I tend to think of energy and momentum as two measures of the same underlying "thing", one being a distance-based measure and the other being a time-based measure - we divide by c or distance over time to switch from one measure to the other. If I call it stress-energy for convention, at the fundamental level I take the view that it's something inseparable from space itself, but you can only "see" variations in energy density. Dark energy however is the exception to this. A universe with a homogeneous stress-energy density still expands, because this stress-energy is akin to an innate spatial pressure.

[amrit]

regarding physics one of the most intelligent questions I ever heard.
I do not know.
Maybe back in space !

[Democritus]

I agree with amrit. A fascinating discussion here. And civil. While learning lots, I may need to reread through this topic several times to have a better understanding of many issues raised. Thank you all. One question. I seem to remember reading somewhere that the Hubble/galactic/universal redshift has little or nothing to do with the Doppler effect. Is this true?