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This started out when I was thinking about what forums posts would be suitable for an April Fool’s day joke but then it is January, when people start thinking about losing weight after all that Christmas excess, so I thought it might be appropriate now. After I had come up with this silly title, the proposal got me thinking and I wondered actually if it wasn’t so silly after all. Bear with me, as I am going over some ideas that some people are familiar with, but others not.
Ok, so not losing weight but losing mass. We talk about losing weight but we mean losing mass. One of the problems we have with cosmology at the moment (that is the study of the Universe and all its contents) is that we have a theory which fits the data, the lamda-CDM model, but it has two components that we have deduced but never actually detected. The first is dark matter and the second is dark energy. Dark matter and dark energy in the lamda-CDM model of the universe make up about 95% of all the universe, the remaining 5% of matter which we would call normal (the stuff that makes up stars, gas, dust and ultimately us) makes up the rest. It is only this 5% that we can so far detect, the rest (the majority) has evaded detection except by its gravitational influence.
The lamda-CDM model was once the CDM model. CDM stands for cold dark matter. We have known for a long time that there is a lot of missing matter out there since Fritz Zwicky looked at the motions of galaxies within clusters and the rotation curves of galaxies in the 1930s. In fact it was Zwicky who termed the phrase “dark matter” in the first place. Basically galaxies in clusters and stars in the outer parts of galaxies are moving too fast if we assume they are bound in place by the gravitational pull of ‘normal’ matter.
Then in 1998 with the observation of supernovae in distant galaxies by the Hubble Space Telescope came another problem. The distances to these ‘standard candles’ seemed to imply that the expansion of the Universe is accelerating at the current time. This was a total surprise. Up until that point we had the notion that there was the ‘Big Bang’ and from this initial point in time all the universe was kind of being blown apart. However, there is all this mass that we can see (or not see) in the universe, so its gravitational influence should be slowing this expansion down. Instead, what has been inferred is that it is actually speeding up. That was when the cosmological constant (lamda) was added to the model to explain the acceleration. Actually, Einstein called the cosmological constant his “greatest ever mistake” but I won’t go into that now!
So here is my idea that people who like this sort of thing can think about. What if we could get rid of one of these big unknowns which we can’t detect (dark energy) and instead consider whether the Universe is losing mass as time passes. I reckon (though I haven’t put this into any equations of motion) that mass loss in a model of the universe would probably mimic accelerated expansion. Perhaps dark matter has these properties? Why not? If you can’t detect something how can you say it hasn’t? Something to mull over and for those who like equations something to try out.
Duncan
Stars loose mass processing simple elements into more complex ones. Our Sun loses about 4 million tonnes of mass per second doing this. Multiply by the number of stars in the universe….
Stars loose mass processing simple elements into more complex ones. Our Sun loses about 4 million tonnes of mass per second doing this. Multiply by the number of stars in the universe….
The mass is not lost. It is converted into the mass of the photons which are emitted by the Sun.
Photons have no rest mass but they possess relativistic mass according to the famous E=mc²
Duncan, this is an interesting idea. For the so-called ‘benchmark universe’, matter and lambda, the scale factor, a(t), is proportional to (sinh(t))^(2/3). So let’s try and see what the Friedmann equations look like if we keep this evolution of the scale factor, but restrict it to one component, which I assume is matter. We then get H^2 is proportional to (coth(t))^2, which I think means that if the matter density is proportional to coth(t), instead of the normal a^-3, we get the same evolution of the scale factor as we do with the benchmark universe. And of course, for large t, (coth(t))^2 tends to 1, which means H tends to a constant, i.e a de Sitter universe. And this is how we expect our benchmark universe to evolve over the long term. Adam
Duncan, this is an interesting idea. For the so-called ‘benchmark universe’, matter and lambda, the scale factor, a(t), is proportional to (sinh(t))^(2/3). So let’s try and see what the Friedmann equations look like if we keep this evolution of the scale factor, but restrict it to one component, which I assume is matter.
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The universe has undoubtedly lost mass-density since the good old days. That is very much not the same as losing mass. And, as I noted, losing matter is not the same as losing mass.
It is extremely important to be precise in one’s terminology when discussing situations in General Relativity. For instance, it is very tricky to determine the mass contained within a region of spacetime other than in the context of an asymptotically flat background.
Thanks for the suggestion Bill. I apologize that my use of the words “mass loss” is close to the term that is often used for stars. Stars, as you say, do lose mass all the time through nuclear burning but also through the stellar winds and evolutionary scenarios. Unfortunately, as Paul says, all that material and heat will just dissipate into another part of the universe and radiation and matter still contribute to the Universe’s gravity through Einstein’s general relativity theory. My idea of mass loss is a bit bonkers really. All of our notions of matter/energy are that this is a conserved quantity. You can’t just magic it away. However, in my defense I would say that we know very little about what the properties of dark matter are and so who is to say what it does. Also, in the past, theorists have had models where they consider the creation of matter as in the steady-state theory of Bondi, Gold and Hoyle (1948). So, if you can consider creating it, why not consider destroying it? Mine idea would be a big bang theory with reverse steady-state!
For the so-called ‘benchmark universe’, matter and lambda, the scale factor, a(t), is proportional to (sinh(t))^(2/3).
Hi Adam. Thanks for taking this on and replying to my wacky ideas! To be honest I am trying to catch up with where you are with your understanding. I didn’t realize that in the matter dominated era in which we are now the scale factor a(t) for a lamda-CDM model could be so neatly expressed as a sinh(t) function. I found this paper (pdf) on the internet which I found helpful. I think their equation (5) is what you are referring to. What a beautifully elegant result! I always assumed that a model with lamda would be difficult to compute. So yes, as you say, this would be the benchmark to compare to. It has two nice asymptotic forms. When H0 t is << 1 the form is as in equation (6). The lamda term becomes negligible and a(t) is proportional to (t)^(2/3) which is like the Einstein-de Sitter model. When H0 t is >> 1 the form is as in equation (8) where the lamda term dominates and a(t) is proportional to exp(k t) where k is a constant which is like the de Sitter expansion model. I hope I have got this right!
I am going to split my replies due to issues of losing my posts when editing them.
A fascinating discussion – and I am looking forward to the conclusion as I try to lose weight every year around this time and would like some tips on how to do better in future!
AlanA fascinating discussion – and I am looking forward to the conclusion as I try to lose weight every year around this time and would like some tips on how to do better in future!
Hi Alan. I would like to help you with your weight-loss plan, however, I think dark matter decay may not help you with your regime. I don’t think there is really enough of it in each of us to be helpful. This article https://www.universetoday.com/15266/dark-matter-is-denser-in-the-solar-system seems to imply that there might only be about 0.0018% mass of the earth in the whole solar system and I reckon, though I haven’t calculated what that equates to per meter cubed, that this doesn’t amount to much in each of us. Perhaps, a more effective way would to lose weight would be to cut your nails as did Tony in an episode of Men Behaving Badly that I recall.
Duncan.
PS Sorry about the edits – having trouble with my bbcodes!
Thanks Duncan. I always suspected that cosmology would come to nought – or close to nought – in the end.
AlanOn a slightly more serious note, and writing as a non-physicist, there seems to me something rather suspect about saying ‘Our model works – but only if we invent entities x and y.’ Might it not be an alternative to say, ‘The anomalies are so great that it looks as if our model doesn’t work. Perhaps it’s time to re-examine fundamental axioms and buil a new model.’ Could we perhaps be heading for an exciting ‘paradigm-shift’?
Alan
(paradigm shift – see T.S.Kuhn, ‘The Structure of Scientific Revolutions’ for anyone unfamiliar with that language.)Dear Duncan, yes, that is the correct equation. I find it fascinating that a two component matter/lambda universe can be modelled with such a simple expression. But this is not restricted to matter/lambda. Other two component universes can be similarly modelled.
Hi Adam. I have been messing about with some of the equations from that paper I mentioned above for the last few days. I thought, perhaps, that if the mass loss from the universe could be written into omega (matter) in equation (1) as something like omega (matter) = -kt + c for some time interval between, say, t1 and t2 (constant k>0 and c to be determined), then we could substitute this into equation (1) with omega (lamda) = 0 (i.e. no dark energy component but instead the matter density is decreasing constantly with time, that is the universe is losing mass). I found, though, that this doesn’t work and so it kind of blows my idea out of the water! The issue is that the second time derivative of the expansion factor d^2 a(t) / dt^2 < 0 which means that even though the universe continues to expand it does so at an ever decreasing rate. Of course, for the model with lamda the change in the rate of expansion goes from decreasing to zero to increasing.
I hope this makes sense.
On a slightly more serious note, and writing as a non-physicist, there seems to me something rather suspect about saying ‘Our model works – but only if we invent entities x and y.’ Might it not be an alternative to say, ‘The anomalies are so great that it looks as if our model doesn’t work. Perhaps it’s time to re-examine fundamental axioms and build a new model.’ Could we perhaps be heading for an exciting ‘paradigm-shift’?
Alan – agreed. The problem is that the standard model of cosmology works very well and it matches observations from very early times until now. It means that people are reluctant to accept a paradigm shift until there is overwhelming evidence to the contrary. It is like having a black box which predicts results for an experiment. If it keeps predicting the right results you might not be tempted to get your screwdriver out and fiddle with its innards in case you mess it up. Interestingly there are a few things on the horizon that may cause concern. One is the so called “Hubble Tension” (see for example https://www.scientificamerican.com/article/hubble-tension-headache-clashing-measurements-make-the-universes-expansion-a-lingering-mystery/) and the other would be if the James Webb Space Telescope starts seeing lots of well-formed galaxies at very high redshifts (see, for example, https://www.scientificamerican.com/article/jwsts-first-glimpses-of-early-galaxies-could-break-cosmology/)
It seems that the Universe may contain a lot of quantum entanglement. This must be a form of information and information bits have an energy cost. As energy equates to mass, I wonder if this contributes to the missing mass problem.
It seems that the Universe may contain a lot of quantum entanglement. This must be a form of information and information bits have an energy cost. As energy equates to mass, I wonder if this contributes to the missing mass problem.
I am sorry I never got around to replying to your comment however I have just seen this article https://www.quantamagazine.org/physicists-use-quantum-mechanics-to-pull-energy-out-of-nothing-20230222/#comments and it makes interesting reading and may be relevant to what you say.
Duncan
I wonder if what we need, in view of recent discoveries by the JWST of massive galaxies only 500 million years after the Big Bang, is a revival of the Steady State theory of cosmology, or some version of it. The detection of evolved galaxies further and further back in time through advancing telescope technology (that actually was going on for some time before JWST) does not fit with the standard model, and was not predicted.
The main discovery that caused the Steady State Theory to loose out against the Big Bang Theory in the 1960s was the discovery of the cosmic microwave background. But could there be some other explanation for that than the Big Bang, I wonder?
A reversion to the Steady State Theory is an interesting possibility.
On the issue of ‘whether the Universe is losing weight’, surely the Universe can be neither losing nor gaining weight because it, by definition, contains everything there is. There is nowhere for any additional weight to come from, and nowhere for it to go.
Simplistic, I know. But sometimes Occam’s Razor comes in handy, especially in the face of quantum entanglement.
On a personal note, I still haven’t lost any weight which perhaps is evidence of the plausibility of my contention and a good reason for me to give up trying!
Alan
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