(December 2, 2015 at 5:28 pm)Quantum Wrote: However, cosmic expansion removes energy from the universe via the redshift.

Can you expand upon this please? I don't understand the "removes" part. Removed to where?

(December 2, 2015 at 5:28 pm)Quantum Wrote: Mass is simply the measure of how much energy of any form is contained in an object (*). Energy is conserved at short time spans, but can be converted and in particular, energy which appears as mass, can be freed from its confines and converted into other types. However, cosmic expansion removes energy from the universe via the redshift.

(*) This holds always. For example, a spring under tension has more mass than a relaxed one, precisely differing by the stored energy divided by c^2

I thought Friedman equations shows energy is conserved in the entire expanding universe despite the red shifting of the photons.

(December 2, 2015 at 4:29 pm)mh.brewer Wrote: Tibs, how do you "loose energy"? My understanding is that it may take a higher amount of energy to make the transformation to the end product. It's just that the end product does not contain all the initial energy. In a closed system the total amount of energy would still exist, just not necessarily in the transformed product. If course I could be wrong, ain't no ricket scientwist.

"Lose" is probably the wrong word to use, but ultimately although the total amount of energy would still exist, some of that energy would be seen as "wasted" in the form of heat / light, etc.

Ultimately, the more energy transfers that take place, the more wasted energy, and after a period of time, that energy spreads out evenly across space, resulting in the heat death of the universe.

(December 2, 2015 at 5:57 pm)Tiberius Wrote:

(December 2, 2015 at 4:29 pm)mh.brewer Wrote: Tibs, how do you "loose energy"? My understanding is that it may take a higher amount of energy to make the transformation to the end product. It's just that the end product does not contain all the initial energy. In a closed system the total amount of energy would still exist, just not necessarily in the transformed product. If course I could be wrong, ain't no ricket scientwist.

"Lose" is probably the wrong word to use, but ultimately although the total amount of energy would still exist, some of that energy would be seen as "wasted" in the form of heat / light, etc.

Ultimately, the more energy transfers that take place, the more wasted energy, and after a period of time, that energy spreads out evenly across space, resulting in the heat death of the universe.

Maybe another way of thinking about it is energy itself is useless for doing anything no matter how much of it there is.   To make energy do things requires the energy to be unevenly distributed to start with.  Every time something is done with the energy the energy becomes more evenly distributed then before.

Eventually when enough things had been done throughout the universe to even out the distribution of energy, the energy in the universe becomes too evenly distributed throughout the entire universe for anything further to be done anywhere in the universe.  When this happens the heat death of the universe occurs.

So total amount of energy never changed.  But the amount of energy that can do work eventually all went away.

A given chunk of matter falling into a black hole can radiate away (as energy) up to 40% of it's mass.

(December 2, 2015 at 5:44 pm)Anomalocaris Wrote:

(December 2, 2015 at 5:28 pm)Quantum Wrote: Mass is simply the measure of how much energy of any form is contained in an object (*). Energy is conserved at short time spans, but can be converted and in particular, energy which appears as mass, can be freed from its confines and converted into other types. However, cosmic expansion removes energy from the universe via the redshift.

(*) This holds always. For example, a spring under tension has more mass than a relaxed one, precisely differing by the stored energy divided by c^2

I thought Friedman equations shows energy is conserved in the entire expanding universe despite the red shifting of the photons.

I don't immediately see how the Friedman equations say something about that, but maybe you can be more specific. They tell us how the scale factor of the universe changes with time for a given amount of energy density in the universe. They have to be supplemented by the equations of state which tell us how the energy density changes with the scale factor. Nonrelativistic matter is diluted by the increasing volume ~a^3 and its energy density therefore goes with a^-3, dark energy has constant density, and relativistic matter ("radiation") is diluted as well as redshifted and goes with a^-4. If we assume for now that the universe is finite in size, the total amounts of both dark energy and radiation change as the universe expands, i.e. the scale factor a gets larger: dark energy increasing its total energy with a factor a^3, and radiation decreasing with a factor a^-1.

The question is now whether one can extend our notion of energy such that it is conserved again. People have thought about whether maybe geometry itself can be assigned an energy density (roughly, but not quite, curvature being a form of energy), and one result is the Landau-Lifshitz-Pseudotensor, which provides a notion of energy stored in the geometry. The Landau-Lifshitz contribution plus all the matter and dark energy and radiation jointly, are conserved again. But matter and energy alone, in the conventional sense, as far as I know, aren't. But I'm happy to hear more points of view on this very subtle topic.

(December 2, 2015 at 5:35 pm)mh.brewer Wrote:

(December 2, 2015 at 5:28 pm)Quantum Wrote: However, cosmic expansion removes energy from the universe via the redshift.

Can you expand upon this please? I don't understand the "removes" part. Removed to where?

The idea is that the universe expands, and you send a photon on its way. Once it reaches the destination, it will be redder, i.e. will have lost energy because the wave was stretched. This way, we seem to lose energy as the universe expands. For example, the photons in the cosmic microwave background which we observe now, had 1100 times the juice when they went on their voyage 13.7 billion years ago. For the question where this energy goes see my post above (note that when we ask the question: "where does the energy go", we implicitely assume that it is conserved, because otherwise it can just vanish or appear without having to "go anywhere").

(December 2, 2015 at 5:28 pm)Quantum Wrote: Mass is simply the measure of how much energy of any form is contained in an object (*). Energy is conserved at short time spans, but can be converted and in particular, energy which appears as mass, can be freed from its confines and converted into other types. However, cosmic expansion removes energy from the universe via the redshift.

(*) This holds always. For example, a spring under tension has more mass than a relaxed one, precisely differing by the stored energy divided by c^2

somewhere in my reading, it was suggested that bosons (energy) are massless particles, while fermions (matter) have mass. To say that mass IS energy let's me know there's something I'm not understanding.

(December 3, 2015 at 8:18 am)Rhondazvous Wrote:

(December 2, 2015 at 5:28 pm)Quantum Wrote: Mass is simply the measure of how much energy of any form is contained in an object (*). Energy is conserved at short time spans, but can be converted and in particular, energy which appears as mass, can be freed from its confines and converted into other types. However, cosmic expansion removes energy from the universe via the redshift.

(*) This holds always. For example, a spring under tension has more mass than a relaxed one, precisely differing by the stored energy divided by c^2

somewhere in my reading, it was suggested that bosons (energy) are massless particles, while fermions (matter) have mass. To say that mass IS energy let's me know there's something I'm not understanding.

That statement is simply wrong. Of the four most massive elementary particles known, three are bosons - the Higgs, the Z and the W. Only the heaviest, the Top Quark, is a Fermion.

The only conceptual differences between bosons and fermions is that the latter have half integer spin and adhere to the pauli exclusion principle - that's it.

(December 3, 2015 at 9:24 am)Quantum Wrote: That statement is simply wrong. Of the four most massive elementary particles known, three are bosons - the Higgs, the Z and the W. Only the heaviest, the Top Quark, is a Fermion.

The only conceptual differences between bosons and fermions is that the latter have half integer spin and adhere to the pauli exclusion principle - that's it.

Thanks, One more question (I hope) and I shall understand this better.

Since mass is the measure of energy, how can the most massive particle be a fermion? In fact, how can any fermion have mass? Unless mass is the interplay of energy and matter. If that is the case (caveat for what follows: it may not be what actually happens. I'm guessing, so trash it as it deserves. My feelings will not be hurt)then when energy is converted into matter there will be less energy actually converted than was originally present, while the unconverted energy acts as a catalyst, bringing about the conversion. Is that the energy that is lost or that interacts with the new matter to give it mass?