For object 3.26 million light-years away, light redshifted by 70 km/s

[PainterGuy]

TL;DR Summary

I was reading an article and needed some help to understand a part of it.

For every 3.26 million light-years away an object is, its light is redshifted by approximately an additional 70 km/s. For historical reasons, astronomers rarely use light-years, but rather more frequently speak in terms of parsecs, where a parsec is about 3.26 light-years. When you hear the term “megaparsec,” abbreviated Mpc, just translate that in your head into “about three and a quarter million light-years.” The most common way to express the expansion of the Universe is in terms of kilometers-per-second-per-megaparsec, or km/s/Mpc.

Source: https://bigthink.com/starts-with-a-bang/fast-space-expanding/

I need help with the part in red. What does it mean when it says light is redshifted by 70 km/s? When the redshift occurs the wavelength increases which is measured in meters or kilometers. I don't understand the "per second" part? Could you please help me with it?

Informally speaking, as a layman, I understand that energy conservation is not a fundamental law. It only holds in a same inertial frame of reference. It doesn't hold in two different inertial frames of reference. Also It doesn't hold in an accelerating frame of reference. So, when a photon travels through expanding space, it gives off a part of its energy to the expanding space. If the space ever starts contracting back, the photon's given off energy will be returned back in some way. Is my thinking okay?

Thanks for the help, in advance!Helpful link(s):
1: https://www.forbes.com/sites/starts...otons-redshift-due-to-the-expanding-universe/

 

[Orodruin]

First of all, you have to take on board that the description is quite rough for reasons of popularization.

When they are referring to redshifted by another 70 km/s they refer to the velocity v in the Doppler factor $\sqrt{\frac{c+v}{c-v}}$. The redshift is that of increasing v by 70 km/s per parsec. It should be noted that using this only works relatively closeby in cosmological terms.

Summary:: I was reading an article and needed some help to understand a part of it.

Informally speaking, as a layman, I understand that energy conservation is not a fundamental law. It only holds in a same inertial frame of reference.

This is not a good understanding. Energy is not conserved in cosmology, but for other reasons. In special relativity is conserved. You are confusing being conserved (always the same in a given reference frame) with being invariant (being the same in different frames).

Summary:: I was reading an article and needed some help to understand a part of it.

So, when a photon travels through expanding space, it gives off a part of its energy to the expanding space.

This is not an accurate description.

 

[phinds]

... when a photon travels through expanding space, it gives off a part of its energy to the expanding space

No. It doesn't "give off" the energy to anything. The measure of the energy just changes. You are trying to apply conservation of energy where it doesn't apply.

 

[Ibix]

So, when a photon travels through expanding space, it gives off a part of its energy to the expanding space. If the space ever starts contracting back, the photon's given off energy will be returned back in some way. Is my thinking okay?

You will find descriptions of the red shift in such terms. However, they presuppose some form of "energy of the gravitational field" with which light can exchange energy. That approach works fine in some circumstances (we routinely use it to justify gravitational red shift near Earth, for example), but cosmology is not one of those circumstances. You can't define an energy of the gravitational field in an expanding universe, so you can't talk about light exchanging energy with it.

However, some physicists say that you can define a global energy in a cosmological context. The ways they do it are very far from universally accepted as legitimate (my limited understanding is that they tend to privilege one choice of definition of "space", which is very hard to swallow for most physicists), but if you do accept it then cosmological red shifts as energy exchange is fine. It would be nice if popsci writers would flag when they are moving out of generally accepted physics and into contentious areas but, as in this case, they often don't.

If the universe is closed then it will eventually start to contract. If so, and if we're still around then, we will see cosmological blue shifts, yes.

 

[Orodruin]

If the universe is closed then it will eventually start to contract.

This is not generally true. For example, a closed universe with a cosmological constant only will always remain closed (but get closer and closer to flat due to accelerated expansion) but grow exponentially at large times.

 

[PainterGuy]

When they are referring to redshifted by another 70 km/s they refer to the velocity v in the Doppler factor $\sqrt{\frac{c+v}{c-v}}$. The redshift is that of increasing v by 70 km/s per parsec. It should be noted that using this only works relatively closeby in cosmological terms.

Are you referring to the equation in yellow below?

Source: https://en.wikipedia.org/wiki/Redshift#Doppler_effect

This is not a good understanding. Energy is not conserved in cosmology, but for other reasons. In special relativity is conserved. You are confusing being conserved (always the same in a given reference frame) with being invariant (being the same in different frames).

Thanks for the correcting me. So, should I say that energy is a conserved quantity in the same inertial frame of reference and it is invariant which means its value would change in a different inertial frame of reference?

Also, is it correct to say that energy is not a conserved quantity in an accelerating frame of reference since two persons in such a frame of reference could measure different values for energy?

This is not an accurate description.

but cosmology is not one of those circumstances. You can't define an energy of the gravitational field in an expanding universe, so you can't talk about light exchanging energy with it.

It wouldn't be wrong to say that not much is known why the space is really expanding, dark energy and how it works and where it comes from etc. So, if it's said that photons exchange energy with expanding space, why is it so wrong? What's the other explanation? Where does the photons' energy go? If the answer is too hard for a layman then never mind.

Thank you for your help and time!

 

[Orodruin]

Thanks for the correcting me. So, should I say that energy is a conserved quantity in the same inertial frame of reference and it is invariant which means its value would change in a different inertial frame of reference?

No. Energy is conserved (it is constant in time for a given reference frame), but not invariant (its value changes depending on the frame). This is true in Newtonian physics as well as in special relativity.

Are you referring to the equation in yellow below?

That is just a trivial rewriting of what I gave, yes.

Also, is it correct to say that energy is not a conserved quantity in an accelerating frame of reference since two persons in such a frame of reference could measure different values for energy?

It is unclear exactly what you would mean by an accelerated reference frame. Curvilinear coordinates are much more involved than the typical inertial reference frames and statements will need to be tailored for that.

Where does the photons' energy go? If the answer is too hard for a layman then never mind.

It does not "go" anywhere. Energy is simply not globally conserved in general relativity. In some cases it is not even relevant to talk about a global energy.

 

[Ibix]

Where does the photons' energy go?

We don't know any way to write a global energy conservation law in arbitrary spacetimes in general relativity. That means that energy is not globally conserved, so the energy doesn't have to go anywhere.

Local conservation of energy still happens in GR. You just can't, in most cases, leverage that into the kind of global law you'd need to discuss energy conservation for light traveling long distances.

 

[PainterGuy]

but not invariant (its value changes depending on the frame). This is true in Newtonian physics as well as in special relativity.

Thank you. Yes, I agree. There was a mistake. I wanted to say "not invariant".

It is unclear exactly what you would mean by an accelerated reference frame. Curvilinear coordinates are much more involved than the typical inertial reference frames and statements will need to be tailored for that.

For me even a car which is constantly accelerating is an accelerating frame of refer. In such a frame of reference, energy is not conserved at different times.

That means that energy is not globally conserved, so the energy doesn't have to go anywhere.

Thank you. Does such a thing happen in any other case? When a far away emitted that photon, from Earth's perspective, it had a certain energy. But after passing through an intermediary space, something happened to the energy of that photon. Suppose, you fire a bullet from under a water tank. The bullet had a certain energy when it was fired but between passing through the water tank and finally getting to the surface, it has lost some energy. I'm sorry but I'm still confused but I do understand these topics are hard to understand for a layman. Thanks.

 

[phinds]

You are STILL wanting to apply conservation of energy where it doesn't apply. See post #3

 

[Orodruin]

For me even a car which is constantly accelerating is an accelerating frame of refer. In such a frame of reference, energy is not conserved at different times.

No. The car is not an accelerating frame. In Newtonian physics you can construct an accelerating frame in which it is at rest. It is not as simple in relativity because there are many different ways to construct curvilinear coordinates on spacetime. Most constructions do not worl globally.

When a far away emitted that photon, from Earth's perspective, it had a certain energy.

No. Big misconception. There is no way in GR to assign an energy to anything that is not colocated. Any photon in itself does not have an energy. It only has an energy relative to a colocated observer.

 

[Ibix]

For me even a car which is constantly accelerating is an accelerating frame of refer. In such a frame of reference, energy is not conserved at different times.

A single point (your car's location) isn't enough to define a reference frame because it doesn't say what all the other fixed points of that frame are doing. If your car is moving inertially and you say you want an inertial frame then you have defined a frame: all other fixed points are keeping pace with your car. In Newtonian physics you can define a rigidly accelerating frame in the same way (all other fixed points keep pace with your accelerating car), but that doesn't work in relativity because there isn't an unambiguous notion of "at the same time" for you to say that all other fixed points of the frame have the same velocity as you at the same time. So you have to be very clear about exactly how you are defining simultaneity before you can make sweeping statements about energy conservation.

And all of that is assuming flat spacetime. Curved spacetime makes everything harder.

Does such a thing happen in any other case?

In any non-static spacetime, which is to say pretty much anything that isn't an eternal never-changing idealisation. That does mean that (in principle) energy conservation doesn't work on Earth, but the error is incalculably small so in practice it works fine.

When a far away emitted that photon, from Earth's perspective, it had a certain energy.

No it didn't. Sure it had a well defined energy as measured by nearby observers, but not according to distant observers.

The problem is that energy is a component of the energy momentum four vector and you can't compare vectors in one place to vectors in another, so you need to (notionally) transport one vector to the other and compare them. There's a unique way to do that in flat spacetime, but not in curved spacetime. That means that in curved spacetime "the energy of that thing over there" is only uniquely defined for observers at the thing, and not for anyone else.

 

[jbriggs444]

For me even a car which is constantly accelerating is an accelerating frame of refer.

One needs to exercise a bit of care.

In ordinary Newtonian mechanics or in the flat space-time of Special Relativity, there is a natural way to use a single observer and establish an associated frame of reference -- the observer's "rest frame".

If the observer is inertial, all is well. The observer's rest frame is an inertial coordinate system that spans all of space and time. Teachers and textbooks often tolerate a bit of sloppiness. We can equate an inertial observer with that observer's inertial rest frame.

However, if the observer is accelerating, things get more complicated. One can anchor a coordinate system and a standard of simultaneity to the observer. But now one has additional choices to make.

One can let the reference frame coast inertially while the observer continues accelerating. This would be a "tangent inertial frame". Of course, this frame fails to capture the observer's acceleration.

Or one can glue the coordinate system to the observer. The standard result is "Fermi Normal Coordinates". The problem is that these coordinates are only valid near the observer. Stray far enough away from an accelerating observer's "world tube" and the coordinates behave badly. You get coordinate singularities or coordinate time going in the opposite direction to proper time.

Those are not the only choices.

The bottom line is that an accelerating observer does not uniquely define an "accelerating frame of reference" and not necessarily one which spans all of space and time. So it is not proper to say that an accelerating observer "is" a frame of reference.

Edit: Note that @Ibix had already made this point.