[Sally Le Page (OP)]

Mark wants to know:

Since the Universe is expanding and light stretches across it as it does so becoming more red, what happens to the lost energy when the shorter wavelength, higher energy light towards the blue end of the spectrum is shifted into lower energy red wavelengths?

Do you know the answer?

[Halc]

Since the Universe is expanding and light stretches across it as it does so becoming more red, what happens to the lost energy when the shorter wavelength, higher energy light towards the blue end of the spectrum is shifted into lower energy red wavelengths?

Energy conservation is a property of (among others) an inertial reference frame, and is not conserved in a metric with expanding space, so the energy is gone. Similarly a rock moving at a nonzero peculiar speed will slow down without any external forces or reaction. The kinetic energy is lost.

Consider the same light in an inertial reference frame, say the 'redshifted' light from a galaxy 2 billion light years away, in the inertial frame of our solar system, and that light didn't lose energy at all and was redshifted in that frame from the moment it was emitted due to the recession velocity of the emitting galaxy.

Heat is another example. Uniformly distributed heat of stationary material in an inertial reference frame has nowhere to go and will not cool over time, but uniformly distributed heat of stationary material in an expanding frame will cool due to the dropping of the pressure/heat-density of the material. This thermal energy doesn't go anywhere since it is already everywhere in both cases.

[hamdani yusuf]

Similarly a rock moving at a nonzero peculiar speed will slow down without any external forces or reaction. The kinetic energy is lost.

What does it mean?
Will the rock eventually stop?

[Halc]

Similarly a rock moving at a nonzero peculiar speed will slow down without any external forces or reaction.

What does it mean?
Will the rock eventually stop?

In the absence of external forces on it (and there is always nearby mass accelerating it, so the condition is unrealistic), the rock will over time approach arbitrarily close to zero peculiar velocity but never reach it. Similarly, light will redshift to arbitrarily low energies but never reach zero.

Interestingly, I cannot see angular kinetic energy reducing, so a spinning rock (at say 10 RPM) will seemingly spin at 10 RPM forever in the absence of external torque. The expanding universe doesn't drain that.
I'm not sure of this. Counter-arguments welcome.

Arguably, matter eventually breaks down and thus our spinning rock cannot be a rock forever, so eventually it becomes something other than a spinning rock (radiation??) whose energy is in fact consumed by the expanding universe.

[Eternal Student]

Hi.

Energy conservation is a property of (among others) an inertial reference frame, and is not conserved in a metric with expanding space, so the energy is gone.

   That's OK and expresses the essence of the issue to the OP.

Consider the same light in an inertial reference frame, say the 'redshifted' light from a galaxy 2 billion light years away, in the inertial frame of our solar system, and that light didn't lose energy at all and was redshifted in that frame from the moment it was emitted (due to the recession velocity of the emitting galaxy).

   Minor note:   I think you (Halc) accidentally missed a word like "emitted" or "released" in your statement.  I've taken some liberties and edited your quote.  Please check you're happy with it.

    Anyway, if that is what you meant then I'm afraid it's still little bit suspect, Halc.  In a spacetime with a metric for expanding space, we can only define inertial frames locally.   We cannot extend an inertial frame centred on our own solar system out to cover a galaxy that was 2 billion light years away even if we wanted to.   In particular, objects at a great distance from the origin of that frame would not behave as if they were in an inertial frame.
   
   Hence, we are UNABLE to determine the frequency of the radiation at the point of release by a distant galaxy using one consistent frame for both the place of emission and the place of reception.  For example, a redshift is not adequately explained by a Doppler effect and special relativity alone.
   We must use General relativity to fully explain the redshift of distant galaxies.  In GR, inertial reference frames are defined differently from SR, they are local and cannot be extended to a universal inertial frame (except for some trivial examples of a metric, which the expanding space metric is not one of).

    If you were going to talk about inertial frames in answer to the OP, then you could try something like this:
   We know that all inertial frames centred around the distant galaxy will be different to any inertial frame centred around our own solar system.  (That difference is not quite as simple as one frame having a velocity relative to the other, they just are different).  Therefore, there is no reason to assume energy would be conserved since we do not have (and cannot satisfy) the requirement you (Halc) stipulated no matter how hard we try.  There isn't a consistent inertial frame in which to measure the energies at emission and later at reception.

      It just so happens that we can identify local inertial frames at both events (emission and reception).  Using the local co-ordinates would be the most natural way for a person to measure the energy of the light.  This is what most PopSci articles are talking about when they discuss how light loses energy and red-shifts while travelling through expanding space.  It's just unfortuante that there isn't a universal inertial frame and so there's no better way to measure the energy of the light (even if we wanted to).  What is being challenged is not just the principle of conservation of energy but something more fundamental than that - Energy can't always be defined universally or measured independantly of the local environment and the local frame of reference for the object.

  Just to be clear, on anything less than Astronomical scales none of this matters.  Energy can be defined and the principle of conservation of energy can be assumed.

Best Wishes.

[Halc]

I've taken some liberties and edited your quote.

Typo fixed, thanks.

We cannot extend an inertial frame centred on our own solar system out to cover a galaxy that was 2 billion light years away even if we wanted to.   In particular, objects at a great distance from the origin of that frame would not behave as if they were in an inertial frame.

While I agree with your entire post, my upshot was that it was close enough for the purpose of answering the OP. It's why I chose 2 billion and not 20. You need perhaps at least 3 digits of precision to measure the difference between actual measurements and those assuming some inertial frame because the scalefactor is currently quite linear due to the effects of mass density nearly cancelling those of dark energy. It helps if the observed matter is at a similar gravitational potential as here where we measure it.

[Eternal Student]

Hi again,

Interestingly, I cannot see angular kinetic energy reducing, so a spinning rock (at say 10 RPM) will seemingly spin at 10 RPM forever in the absence of external torque. The expanding universe doesn't drain that.
I'm not sure of this. Counter-arguments welcome.

   This is complicated and interesting.  This is what I think would happen (but I've not read anything that would tackle this question directly).

   The expansion of the universe would not change the angular speed, or RPM  of the spinning object.   However it could change the rotational kinetic energy it had.

   We need to know if the spinning object is bound so that the distance from one part of the object to another part of the object never changes with time.  The main alternative would be that the object co-expands with the universe, which I won't consider here.
    If the object was bound and can be treated as a rigid body, then after each complete rotation we can take a snapshot of the object and see how it would look if we overlay a grid that shows the co-moving co-ordinates. 
    Now, since space is expanding, the grid showing co-moving co-ordinates must expand in our snapshots as time evolves  (the distance as determined by the metric between two co-moving points increases with time).
   So we can see that the spinning object has a constant size in terms of length we can measure intrinsically using the metric   BUT  it has a reducing size when expressed in the co-moving co-ordinates.   So the rotational kinetic energy (in the co-moving co-ordinates) decreases.

? Well, that's my best guess anyway.

[Just thinking]

Since the Universe is expanding and light stretches across it as it does so becoming more red, what happens to the lost energy when the shorter wavelength, higher energy light towards the blue end of the spectrum is shifted into lower energy red wavelengths?

The red shifted light is weakened but all the photons are still there blue shifted light is strengthened as it is compressed all the energy remains the same only arriving at different times.

[Eternal Student]

Hi.

@Just thinking,   I'm not sure what you were saying there.
- - - - - - - -

Usually Sally Le Page tells us when the question is answered in a podcast but hasn't done so this time, perhaps she's on holiday.
   Anyway, it does seem to have been answered here:   https://www.thenakedscientists.com/sites/default/files/media/podcasts/episodes/Naked_Scientists_QotW_21.09.13.mp3

    It's about three and a half minutes and by the time the scene has been set, there's about 1 minute of actual answer.   Their basic answer is that there is a lack of time translation symmetry.   It ends with one sentence of waffle (vague comment) about space-time absorbing the energy.   This seems to be an attempt to restore the public confidence that energy is conserved, it's just different.  While the podcast was disappointingly short, that last sentence was actually harmful and you might have been better off without it.  It completely eroded the importance of the only key statement you made - that the conservation of energy does not apply.
    It's easy to criticise and we should spend a moment to recognise the good stuff in the podcast:  It was pleasant and refreshing to have a podcast that focuses on Physics.  It was quite courageous to (almost) publically challenge a long held view that energy is always conserved.

Best Wishes.

[Just thinking]

I'm not sure what you were saying there.

Thanks, Eternal Student for your reply it is just that the question that has been asked is when light is stretched where does the extra energy go I don't understand what the extra energy is but I can only say that the energy that is there remains the same as stretching only delays the arrival time and takes nothing away. The opposite for blue shift this would mean that the light would be compressed and will arrive earlier than expected. No energy gained or lost either way.

[Kryptid]

The red shifted light is weakened but all the photons are still there blue shifted light is strengthened as it is compressed all the energy remains the same only arriving at different times.

That's not true. Photons with longer wavelengths have less energy than those with shorter wavelengths. The speed of light also does not vary with wavelength, so a red-shifted photon will arrive at the same time as a blue-shifted photon.

[Just thinking]

That's not true. Photons with longer wavelengths have less energy than those with shorter wavelengths. The speed of light also does not vary with wavelength, so a red-shifted photon will arrive at the same time as a blue-shifted photon.

Not so true if a star is moving away at a high velocity the light emitted from it will be less extreme this is what makes the redshift. Each photon is arriving later and later due to the star moving away this is the stretching of the light.

[Kryptid]

Not so true if a star is moving away at a high velocity the light emitted from it will be less extreme this is what makes the redshift. Each photon is arriving later and later due to the star moving away this is the stretching of the light.

All right, so long as you understand that light of all wavelengths moves at the same speed.

[Just thinking]

All right, so long as you understand that light of all wavelengths moves at the same speed.

Yes, that is true it is just if the source of the light is moving the light will be either compressed or stretched making the light more intense or weaker. This is the shift and nothing is lost or gained by the shift.

[Eternal Student]

Hi again.

@Just thinking,

   It's difficult and possibly repetitive to explain where you might have gone slightly wrong.
First of all, there's nothing wrong with what you've said at all in situations where a Doppler effect applies and it is just that the source and receiver have some velocity relative to each other.  If space was just flat Minkowski space then what you've said would be perfectly fine.
    The main problem for the expansion of space is that there is no way to determine the velocity of the source relative to the receiver.  Even in situations where both source and receiver seem to have 0 velocity through space (they are co-moving) so that you might reasonably expect them to be at rest with respect to each other,  some redshift is still observed.    To paraphrase this, there is no way to know how much of this "compression" that you describe can be explained just as the movement of the source relative to the receiver.   All we know is that where space expands, each individual photon will be redshifted as time evolves whenever it's frequency is determined in the co-moving co-ordinate system.   It could be that we are using the wrong co-ordinate system but there just isn't a better frame we can use.

     This is complicated, so I'll try to phrase everything another way:
We can divide the universe into a large number of small patches of space.  In each little patch, everything behaves just fine, special relativity and/or flat Minkowski space describes the situation just perfectly.

--|----------- |-----------|----------- |--
  | patch 1 |              |              |
  |              | patch 2 |              |
  |              |              | patch 3 |
--|-----------|----------- |----------- |--

   We can't easily extend a frame of reference from one patch over to cover another patch but it doesn't matter too much:  In each patch there is a frame of reference that seems perfectly natural and the most sensible one to use.    For an expanding universe, what we observe is that when a photon moves from one patch to a neighbouring patch, it is redshifted or seems to lose energy.   The original frequency left the first patch, taking an amount of energy E= hf   out of that patch   but the photon entered the other patch with a lower frequency  v < f   and a corresponding amount of energy E = hv.   So not all of the energy that left the first patch made it into the second patch and we don't really know where the difference in energy went, it didn't seem to go anywhere.   

    It could very well be that we just weren't using the right reference frame in the new patch but there is nothing that we can do about this.   This is where General relativity significantly differs from Special relativity.  We can't pick up the reference frame from patch 1 and use it in patch 2.   For example, we might try and use a different reference frame in patch 2 that is moving toward patch 1.  We can give the photon coming in from patch 1 exactly enough blueshift in this new frame to counter the redshift it would otherwise have had when it moves from one patch to another.  That's great -  BUT  if you glance at the diagram above you'll see that we have made the problem much worse for a photon coming in from the East side (from patch 3 to patch 2).  A photon moving in that direction would now suffer twice the redshift it needed to  (one shift because it changed patches + another shift because our frame for patch 2 is now moving away from the photon).   There is no easy way to define an inertial reference frame for patch 2 where a redshift doesn't occur for a photon coming in from at least some direction.

Best Wishes.

[Kryptid]

This is the shift and nothing is lost or gained by the shift.

Energy is.

[Just thinking]

If we take a given galaxy let's say a billion light years away and we conclude that it is redshifted and we conclude that it is moving away from us at 10% the speed of light what will we see and what will the light do over time. Ok, this hypothetical galaxy is receding from us one light year every ten years so in ten years the light that reaches us will be weaker why is the light weaker I'm glad you asked the light is spreading out and every passing second less of the light will contact us moor and moor of the light will bypass the earth leaving less to contact us. This is just the light getting weaker and has nothing to do with the redshift. The redshift is the light stretching I don't believe the term stretching is really what is happening it is the parcel of light leaving the galaxy that is arriving later and later as the galaxy receeds. So I conclude the light is thining not stretching every second the light takes longer to reach us not because the light is slowing down it's because the light source is getting further away this is the redshift. The Compleat opposite is true for the blueshift.

[Just thinking]

This is complicated,

Thanks Eternal Student for your time and effort trying to explain this problem. It may well be as you have shown but I find it very difficult to see this problem any other way anyway if I am wrong maybe the fog will lift and I will see things differently.

[Eternal Student]

Hi.

If we take a given galaxy let's say a billion light years away and we conclude that it is redshifted and we conclude that it is moving away from us at 10% the speed of light

    Firstly, what do you mean by moving away from us at 10% the speed of light?
    Most people would assume we can measure the distance between us and the distant galaxy and then see how this changes with time.   In school you would have been told that this formula holds:
     Speed =   

    Is that what you mean?    The rate of change of distance with time   =   10% speed of light =   0.1 c

   For flat space, this is a perfectly sensible idea of speed and it is easily converted into a velocity.  The velocity of an object is just a vector with magnitude equal to the speed and direction given by the direction of travel.

    However, in curved space things are more complicated.  We can still calculate something we can call a speed of recession and it is exactly as described above - it is the rate of change of distance with time.   However, that speed does not convert into a velocity in any sensible way.   It is possible for the distant galaxy to move in a direction that just doesn't exist as a direction we can have in our solar system.  The velocity of the distant galaxy is meaningless when regarded as a velocity that something could have here in our solar system.

   Let's take a simple example of curved space.   The usual example is to consider the surface of a ball.   This will be a 2-Dimensional space.  It's useful because we can embed this space in our usual 3-Dimensional space and then we have a way to see or visualise the curvature.

Here's a ball:



Our space is going to be the surface of that ball.  We exist like little ants, forced to move in ("on" but it will be easier to say "in") the surface of the ball.  We can move along the surface but we cannot move out of the surface.  The 2-D space of the surface is the only thing we can experience.  Now consider a point in our space which we will say is at the North pole of the ball.  At that point in space we can move, or have velocities that are shown in the diagram above.  This is the tangent plane to the ball at the North pole.  The only velocities we can have are contained in what we can call the horizontal plane.  We'll take the North pole to be the location of our own solar system in the universe.
   Next consider a point along the equator of our ball.  I've shown that on the diagram and marked the corresponding tangent plane at that point.  At that point  (which we will take to be our distant galaxy), we can only move (or have velocities) that are contained in the vertical plane.  In particular, there is one direction of movement (straight up and down) that we can have at the equator but we cannot have at the North pole.  If we had this vertical velocity at the North pole it would move us (the ants) straight out of the surface of the ball.  It's not allowed, it's not a velocity that exists at the North pole, we are constrained to move in the surface always.
   
    Now, this is where you should start to recognise some of the problems we run into in curved space.  It is possible for a distant galaxy to be moving in direction that makes no sense at all (like straight down) when we are considering space from our location at the North pole.   It can be moving in a "direction" that does not exist in our solar system.  So we are unable to say that the distant galaxy is "moving away" from us.  There is no direction we can point to and say it was moving in that direction.  It is moving in a direction that is "invisible", "inaccessible" or just "nonexistent gibberish" in the local space that we are located in.   

    None the less, we can measure the distance between our solar system and the distant galaxy - we do this by stretching a piece of thread from us to the distant galaxy and keeping it within the surface of the ball all the way.   So we can observe a change in that distance as time progresses - so we can calculate the quantity described above and called the recession speed.  The recession speed makes sense just as the rate of change of distance with time,  however, it is not the magnitude of any velocity that the distant galaxy had.

   Anyway, these are the problems we run into with space that isn't flat Minkowski space.  For an expanding universe, the distant galaxies aren't really moving "away" from us.  At best, they are moving in a direction that doesn't exist or makes no sense in our local solar system.  All we can establish is that the distance between us and the distant galaxies increases with time.  This is something we can call a recession speed but we must be careful not to assume that the entirety of space in the universe is flat and therefore not to treat that recession speed as if it is a velocity through ordinary flat space.

   I hope this helps or makes some sense.  Best Wishes.

[Just thinking]

Energy is.

How is energy lost as a result of redshift?