Discussion of Dark Matter, Mass, and Relativity

[Quadhelix]

To avoid a derail in the Fanfiction Discussion forum/subforum, I figured that this would be a good place to move the discussion:

Dark Matter does let you explain things, and it was perfectly plausible twenty years ago. We have since then consistently failed to actually find it. My favorite alternative explanation (MOND and its variants) is a modification of gravity for really, really low forces (acceleration actually, but that's less intuitive).

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I actually did a small report on MOND for a class back in undergrad. The particular study I referenced derived its modifications to Newton's law of gravitation by studying the orbits of stars in Andromeda. The professor asked if they had tried applying their modified law of gravitation to other galaxies and I had to admit that I was not aware whether they had.

What later put me off to the idea of MOND is the discovery of at least one dark matter galaxy, which exerts a strong gravitation pull on its neighbors and the stars within it, but contains little to no visible matter. (Side note, when I Googled a source for "dark matter galaxy" just now, I found that scientists had discovered at least one galaxy with little to no dark matter content)

The replication crisis is worse than most people think since it's not just that the US research gets to be seen as the prime source of knowledge, but that scientific theories in general are interpreted in different ways depending on the culture. For an example Matter and Energy are seen as separate but transmutable into each other aspects of reality in most English speaking regions and yet in my own country of Serbia Matter and Energy are seen as two subsets of a greater set. This means that an English speaking scientist will examine Matter and Energy as separate supersets of empirical evidence while a Serbian scientist will see only one superset with two easily definable subsets.

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I'm rather confused here. One of the major discoveries in Relativity is that mass and energy are two different aspects of the same property*. Indeed, my understanding is that certain things that used to be seen as functions of an object's mass (e.g., gravitational interaction) are now seen as functions of the object's total energy.

* One way of looking it is through the full form of the famous "E=mc2​" equation: E2​=m2​c4​+p2​c2​, where p is the momentum of the object. Another way of looking at it is that mass (or "rest mass") is the magnitude/"length" of the object's four-dimensional "energy vector," where total energy is the "time-like" component of the vector and the three momentum components (px​, py​, pz​) are the "space-like" components.

I suspect future school students will laugh at us for postulating such ridiculous things as matter that has mass but somehow doesn't adsorb, emit, or reflect light, because we were too primitive to see outside our little 'all things are matter or energy' paradigm*.

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Side note: "has mass but somehow doesn't adsorb, emit, or reflect light" also describes neutrinos -- they have some slight mass, but do not interact with the electromagnetic force (i.e., with light and phenomena related to light).

 

[Dmol8]

I'm rather confused here. One of the major discoveries in Relativity is that mass and energy are two different aspects of the same property*. Indeed, my understanding is that certain things that used to be seen as functions of an object's mass (e.g., gravitational interaction) are now seen as functions of the object's total energy.

* One way of looking it is through the full form of the famous "E=mc2" equation: E2=m2c4+p2c2, where p is the momentum of the object. Another way of looking at it is that mass (or "rest mass") is the magnitude/"length" of the object's four-dimensional "energy vector," where total energy is the "time-like" component of the vector and the three momentum components (px, py, pz) are the "space-like" components.

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Well if we are using the expanded terms the full Relativity discovery is attributed to both Einsteins: Albert Einstein and Mileva Marić-Einstein. Likewise while the General Theory of Relativity unified the terms Matter and Energy into a single unified subject in English (and most western civilization) scientific communities it has also caused an interesting question to appear in Serbian scientific communities: Since Matter was seen as the sum of stuff that makes up the universe that was made up of Substance and Energy before Relativity and after Relativity there are empirical phenomena that don't fit well into either the Substance or Energy category should we add more categories?

 

[BurnNote]

Let me preface this with a disclaimer: I'm a physicist, but I don't really have any training in astronomy. I'll also try to make it understandable to a layman. Don't hesitate to question me on wrong or unclear points.

I actually did a small report on MOND for a class back in undergrad. The particular study I referenced derived its modifications to Newton's law of gravitation by studying the orbits of stars in Andromeda. The professor asked if they had tried applying their modified law of gravitation to other galaxies and I had to admit that I was not aware whether they had.

What later put me off to the idea of MOND is the discovery of at least one dark matter galaxy, which exerts a strong gravitation pull on its neighbors and the stars within it, but contains little to no visible matter. (Side note, when I Googled a source for "dark matter galaxy" just now, I found that scientists had discovered at least one galaxy with little to no dark matter content)

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See, I haven't actually seen the application of MOND to this. I came across the idea seriously when I found the blog Trition Station. I find his arguments rather convincing, though again, I don't have the training or the time to do a serious weighing of the evidence.

To summarize: The radial acceleration of of galaxies isn't like it should be, given the observed mass and current theories of gravity. This is as close as it gets to a fact.

To solve this, there are two approaches: We don't observe all the mass, ie there's 'dark' mass. Or our theory of gravity is wrong, ie modifing Newtonian dynamics.

Since Relativity is well tested, it's sensible to assume dark mass. But so far, none of the candidates have panned out. Also, using dark matter to actually simulate galaxies can be kind of ugly, since you need to make assumptions about initial distributions and such. Given enough parameters to fiddle with, you can always make it fit.

MOND basically says: There is some universal acceleration under which gravity behaves differently. Thus we have just one extra parameter. We can fit once, and it has to work for all the other galaxies. As it turns out, this works quite well. In my personal opinion, it's sufficiently good that MOND is justified at least on an empirical basis. MOND also has the strong advantage of actually predicting things in advance. I'm not aware of verified dark matter predictions.

For further reading: The MOND pages have a huge list.
If you have an hour, this talk is quite good. It does a way better job that I could, and at a quite understandable level. If you've found the above at all interesting, I suggest this as a starting point.(Completely unrelated, but I did not know Stacy can be a male name.)

Side note: "has mass but somehow doesn't adsorb, emit, or reflect light" also describes neutrinos -- they have some slight mass, but do not interact with the electromagnetic force (i.e., with light and phenomena related to light).

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Ah yes, something worth spelling out: There is dark matter. As in, matter that either doesn't interact with light, or just does it very weakly. But the sources of dark matter we understand just don't account for anywhere near as much as is necessary for the Dark Matter explanation.

Also, since it comes up semi-regularly: Dark Matter and Dark Energy have almost nothing to do with each other.

Well if we are using the expanded terms the full Relativity discovery is attributed to both Einsteins: Albert Einstein and Mileva Marić-Einstein. Likewise while the General Theory of Relativity unified the terms Matter and Energy into a single unified subject in English (and most western civilization) scientific communities it has also caused an interesting question to appear in Serbian scientific communities: Since Matter was seen as the sum of stuff that makes up the universe that was made up of Substance and Energy before Relativity and after Relativity there are empirical phenomena that don't fit well into either the Substance or Energy category should we add more categories?

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I'm sorry, but I'm not sure what you're trying to say. Can you give an example for a phenomenon that doesn't fit Energy or Substance?

 

[Dmol8]

I'm sorry, but I'm not sure what you're trying to say. Can you give an example for a phenomenon that doesn't fit Energy or Substance?

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For a hypothetical example take a look at Gesprensterfelder as a type of theoretical Dark Matter. They don't carry momentum or energy and are not associated with any particle. As such they are neither Substance nor are they Energy. What to do with something like that? And to be clear it's not just Gesprensterfelder. A lot of partial or full explanations for what Dark Matter and/or Dark energy are go outside the current definitions of what Substance and Energy even are. In some cases even the base definitions don't encompass them. As such either Substance and/or Energy will need redefining or we need to introduce more category(-ies) into our definition of Matter.

 

[Shard]

Out of curiosity, does proving MOND necessarily disprove the existence of Dark Matter and vice-versa?

 

[BurnNote]

Out of curiosity, does proving MOND necessarily disprove the existence of Dark Matter and vice-versa?

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First, a bit of terminology: You don't generally "prove" a theory in physics, because you can never be totally certain. Also, even theories that are "wrong" in principle can often be useful. Newtonian mechanics is one example.

But to actually answer the question: Technically no, practically mostly yes. Let me give you an analogy:

The tires of your car got slashed. You have good reason to believe it was either Jake or Jim. If you found footprints of Jake around your car, you'd take that as good evidence that it was Jake. If you find him with a knife with rubber staining, you'd probably close the case right there. However, it is possible that Jim and Jake both independently slashed your tires, just kinda unlikely. Also, if you have video of Jake slashing three of your tires, it's pretty likely that he slashed the fourth as well.

 

[Starfield]

So, I haven't heard of a preference for base six.

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6 leptons + 6 antileptons, and 6 quarks + 6 antiquarks.

 

[macdjord]

MOND basically says: There is some universal acceleration under which gravity behaves differently. Thus we have just one extra parameter. We can fit once, and it has to work for all the other galaxies. As it turns out, this works quite well. In my personal opinion, it's sufficiently good that MOND is justified at least on an empirical basis. MOND also has the strong advantage of actually predicting things in advance. I'm not aware of verified dark matter predictions.

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So how does MOND explain the galaxy that lost all its dark matter in a collision with another galaxy?

 

[BurnNote]

6 leptons + 6 antileptons, and 6 quarks + 6 antiquarks.

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I'm sorry, but that's not a good argument. By the same token, you could argue three (spacial Dimensions, also 6=3*2) or four (fundamental forces, spacial dimensions) or just about any other number. On its own, this is just numerology.

So how does MOND explain the galaxy that lost all its dark matter in a collision with another galaxy?

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The answer is: I don't know. Maybe it does. Maybe it doesn't. Remember my disclaimer, I'm no expert in astronomy.

That said, it should be kept in mind that astronomy has some pretty messy data. Putting too much weight on any one object is dangerous. It succeeds surprisingly well for a large number of galaxies. For some were it doesn't, there are ideas why it doesn't. For others, it might be because MOND is wrong (we know that it's not complete, just like relativity), or because the data is bad, or because we don't understand the theory well enough.

For a hypothetical example take a look at Gesprensterfelder as a type of theoretical Dark Matter. They don't carry momentum or energy and are not associated with any particle. As such they are neither Substance nor are they Energy. What to do with something like that? And to be clear it's not just Gesprensterfelder. A lot of partial or full explanations for what Dark Matter and/or Dark energy are go outside the current definitions of what Substance and Energy even are. In some cases even the base definitions don't encompass them. As such either Substance and/or Energy will need redefining or we need to introduce more category(-ies) into our definition of Matter.

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I'm not particular familiar with this, but it sounds like an obscure edge case of a somewhat non-standard interpretation, more a mathematical artifact than physical reality. However, I can't really claim certainty on that.

However, this is not a Dark Matter candidate. If it doesn't have energy, then it doesn't have mass, and so it isn't relevant for Dark Matter (unless you want to redefine gravity, but then why bother with Dark Matter in the first place?).

 

[Vorpal]

Historically, baryon-acoustic oscillations during the early universe has probably been a much bigger factor in the general acceptance of dark matter than galaxy rotation curves. So something motivated by 'fixing' the rotation curves is not likely to impress. And it doesn't: the standard cosmological model with dark matter does extremely well with the WMAP spectral curve, and MOND doesn't.

And yes, one of the more interesting developments this year is the discovery of galaxies without dark matter. Though morally, it's another extreme end of things like the bullet cluster and dark matter galaxies. The claim that it can all be fixed by fitting one parameter is just obviously wrong, and relativistic MOND-like theories have things like three extra field and an nigh-arbitrary function as extra degrees of freedom. At that point, one would be curve-fitting with a poorly physically motivated model. (Or if we go wider, other ways, like some function of Ricci curvature, which at least semi-respects the symmetries of GTR.)

The standard model model contains light dark matter, and extensions to it nigh-generically predict heavy dark matter. From plain vanilla GUTs to cutting-edge extensions like string theory, this is a pretty generic feature. So my impression is exactly opposite than what started this: as the decades go by, MOND is increasingly fringe and irrelevant, both ill-fitting with wider physics and doing the things it was designed to do less and less well as new astronomical observations pile up.

... Likewise while the General Theory of Relativity unified the terms Matter and Energy into a single unified subject in English (and most western civilization) scientific communities it has also caused an interesting question to appear in Serbian scientific communities: Since Matter was seen as the sum of stuff that makes up the universe that was made up of Substance and Energy before Relativity and after Relativity there are empirical phenomena that don't fit well into either the Substance or Energy category should we add more categories?

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Of course there are: momentum, spin, etc. Seriously, this fetishisation of energy bugs me, and this looks like very outdated philosophy-speak than physics.

 

[BurnNote]

Of course there are: momentum, spin, etc. Seriously, this fetishisation of energy bugs me, and this looks like very outdated philosophy-speak than physics.

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So, I'm not sure the two of you are talking about the same thing.

Energy, linear momentum, rotational momentum and so on all come from fundamental symmetries. If the times t1​ and t2​ aren't fundamentally different, you will have conservation of energy. Same for space and momenta. Things like charge and spin also have symmetries, but those are more abstract. Now, why care about energy in particular? Because we like to predict things, which means we care about time evolution, and that's very closely related to energy. The Hamiltonian essentially is the energy.

 

[Yla]

Also, using dark matter to actually simulate galaxies can be kind of ugly, since you need to make assumptions about initial distributions and such. Given enough parameters to fiddle with, you can always make it fit.

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As someone with a M.Sc. in "simulations", I have seen how the sausage is made.
Successful simulations are good on the 'this model is useful' scale, but a dead zero on the 'this model has anything to do with reality' scale.

*shudders at the memory of some lectures on turbulence modeling, and schedules another therapist appointment for his sense of math*

 

[Vorpal]

Energy, linear momentum, rotational momentum and so on all come from fundamental symmetries. If the times t1​ and t2​ aren't fundamentally different, you will have conservation of energy. Same for space and momenta. Things like charge and spin also have symmetries, but those are more abstract. Now, why care about energy in particular? Because we like to predict things, which means we care about time evolution, and that's very closely related to energy. The Hamiltonian essentially is the energy.

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From context of the statement of the involvement the Einsteins and 'unifying' Matter and Energy, we're talking about the development of special relativity. From the point of view of STR's fundamental relations, it makes no sense to single out energy, and momentum is equally unified; the OP explained this as well. Furthermore, the symmetry group of of STR is Poincaré, the Casimir operators of which are mass, spin, and parity. So you're simply mistaken about spin, and it's no accident why those are the first ways fundamental particles are classified (the other quantum numbers, e.g. charge and isospin, are 'internal', though).

Finally, both the mode of thought and the weird capitalisation are more reminescent of the XIX/early XX century natural philosophy than physics in the last hundred years.

 

[BurnNote]

From context of the statement of the involvement the Einsteins and 'unifying' Matter and Energy, we're talking about the development of special relativity. From the point of view of STR's fundamental relations, it makes no sense to single out energy, and momentum is equally unified; the OP explained this as well. Furthermore, the symmetry group of of STR is Poincaré, the Casimir operators of which are mass, spin, and parity. So you're simply mistaken about spin, and it's no accident why those are the first ways fundamental particles are classified (the other quantum numbers, e.g. charge and isospin, are 'internal', though).

Finally, both the mode of thought and the weird capitalisation are more reminescent of the XIX/early XX century natural philosophy than physics in the last hundred years.

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Ok, now I know we're talking past each other.

 

[Vorpal]

Ok, now I know we're talking past each other.

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What you're saying just doesn't have much to do with anything.

The whole issue of unification of Matter and Energy isn't actual physics strictly speaking, and none of your reference to Noether and Hamilton changes that fact (and is fundamentally wrong regarding spin anyway), especially as they're not even a product of relativity, which was the topic. There are some particles (or fields, if you like), and energy is one of their observable properties, and they have other observables. Matter isn't equivalent nor ever turns into energy strictly (except as a metaphorical description which may be good enough for many purposes); particles turn into other particles.

It is true that in many ways energy has more practical significance than other observables, but it is no more or less 'unified' with matter than a host of other properties.

 

[BurnNote]

What you're saying just doesn't have much to do with anything.

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Dude, you don't have to be rude. And obviously it has to do with something. If it's not the aspect you wanted to discuss, then you should be clearer on what you want to discuss.

The whole issue of unification of Matter and Energy isn't actual physics strictly speaking, and none of your reference to Noether and Hamilton changes that fact (and is fundamentally wrong regarding spin anyway), especially as they're not even a product of relativity, which was the topic. There are some particles (or fields, if you like), and energy is one of their observable properties, and they have other observables. Matter isn't equivalent nor ever turns into energy strictly (except as a metaphorical description which may be good enough for many purposes); particles turn into other particles.

It is true that in many ways energy has more practical significance than other observables, but it is no more or less 'unified' with matter than a host of other properties.

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Just wanna point out: The original starting point for this particular discussion was QM.

I'm not sure why you state it (what it? Presumably the Noether Theorem) is fundamentally wrong for spin. No, spin is not derived from the Noether Theorem, but I never cited that either, and it does derive from the symmetry of the spin group. Same idea.

Now, what is your definition of matter? From context, I assume @Dmol8 means 'mass'. I don't think you do. Hence, talking past each other.

 

[xa na xa]

The standard model model contains light dark matter, and extensions to it nigh-generically predict heavy dark matter. From8 plain vanilla GUTs to cutting-edge extensions like string theory, this is a pretty generic features.

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Does this generic cold dark matter predictability include loop quantum gravity as well?

 

[Dmol8]

I'm not particular familiar with this, but it sounds like an obscure edge case of a somewhat non-standard interpretation, more a mathematical artifact than physical reality. However, I can't really claim certainty on that.

However, this is not a Dark Matter candidate. If it doesn't have energy, then it doesn't have mass, and so it isn't relevant for Dark Matter (unless you want to redefine gravity, but then why bother with Dark Matter in the first place?).

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Um because the Pilot Wave Theory already redefines gravity and removes a need for a chunk of both Dark Matter and Energy, but not all of it.

Historically, baryon-acoustic oscillations during the early universe has probably been a much bigger factor in the general acceptance of dark matter than galaxy rotation curves. So something motivated by 'fixing' the rotation curves is not likely to impress. And it doesn't: the standard cosmological model with dark matter does extremely well with the WMAP spectral curve, and MOND doesn't.

And yes, one of the more interesting developments this year is the discovery of galaxies without dark matter. Though morally, it's another extreme end of things like the bullet cluster and dark matter galaxies. The claim that it can all be fixed by fitting one parameter is just obviously wrong, and relativistic MOND-like theories have things like three extra field and an nigh-arbitrary function as extra degrees of freedom. At that point, one would be curve-fitting with a poorly physically motivated model. (Or if we go wider, other ways, like some function of Ricci curvature, which at least semi-respects the symmetries of GTR.)

The standard model model contains light dark matter, and extensions to it nigh-generically predict heavy dark matter. From plain vanilla GUTs to cutting-edge extensions like string theory, this is a pretty generic feature. So my impression is exactly opposite than what started this: as the decades go by, MOND is increasingly fringe and irrelevant, both ill-fitting with wider physics and doing the things it was designed to do less and less well as new astronomical observations pile up.

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That for starters assumes that the Big Bang Theory is accurate. It is not. For starters we already know that a chunk of the Matter in the universe is not visible from our own reference/observation point and may never be. Why is the assumption that we do in fact see enough of the Universe to be able to theorize about it's origins still accepted?

Also Microwave Background Radiation is assumed to be from the Big Bang yet all the data we have on it is from the last 50 or so years. Please tell me that people at least remembered that interference is a thing and that certain waves we might be able to observe from other points in the universe cancel each other out from our point of view. How much of Dark Matter/Dark Energy/Cold Spot in the Microwave Background Radiation is caused by destructive wave interference from our point of view?

What does morality have to do with extreme ends of possibilities of matter in the standard model?

Also Pilot Wave Theory has been proven non-local since 2010 so the model is about to get changed and probably more complicated in some places and less complicated in others since Pilot Wave Theory doesn't suddenly just disprove Quantum Mechanics in a puff of logic, nor does the opposite happen.

Speaking of non-locality has anyone tested the distance with that property? Like putting sunglasses lenses in orbit around the sun and aligning them to a non-local positioning at distances of light second/minutes instead of just doing the experiment at distances on earth that are negligible in terms of time.

You wrote model twice.

The assumption that MOND is useless because it can't eliminate the need for Dark Matter/Energy I find deeply problematic. Even if it was designed originally as an alternative to such things doesn't mean that the idea that Gravity works differently in different regions of space is without merit. Although the name itself is up there with Phlogiston in terms of topics that were thought trough properly before being tackled. So I'm looking forward to when we figure out what MOND's version of Oxygen looks like.

Of course there are: momentum, spin, etc. Seriously, this fetishisation of energy bugs me, and this looks like very outdated philosophy-speak than physics.

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Really? Momentum? Spin? I'm sorry I'm so horrible at explaining my own language and culture. Substance refers to any piece of Matter that has a particle and Energy in this context refers to Physical Fields. This includes both Momentum and Spin. In fact Spin is the fourth basic Physical Field any piece of Matter has. The basic Physical Fields are know as Quantum Numbers. The First Quantum Number is also known as Bohr's Number and is usually only used in reference to which energy shell of the atom an electron occupies, but there is a value of this number for each subatomic particle it's just that scientists have not found use for such values. The Second Quantum Number is also known as the Orbital Number because it is usually used just to determine the shape of the electron orbits around the atom. Again every subatomic particle has a value of it. The Third Quantum Number is known as the Orbital Magnetic Number since it's value is determined by an observation in a magnetic field and the value of the Second Number for the observed. It is related to the nature of possible vectors for a particle and yet again all subatomic particles have it. The Fourth Quantum Number is known as the Spin Magnetic Number and it depends mostly on the structure of the lattice the subatomic particle is a part of and on the nature of the particle itself (Leptons like the Electron have a base spin 1/2 while Protons still have a base spin 1/2 since they are made from 3 quarks who all three still have a spin 1/2). Of course since they are called Quantum Numbers that does mean that elementary particles and composite particles also have their own values of the Numbers.

So, I'm not sure the two of you are talking about the same thing.

Energy, linear momentum, rotational momentum and so on all come from fundamental symmetries. If the times t1​ and t2​ aren't fundamentally different, you will have conservation of energy. Same for space and momenta. Things like charge and spin also have symmetries, but those are more abstract. Now, why care about energy in particular? Because we like to predict things, which means we care about time evolution, and that's very closely related to energy. The Hamiltonian essentially is the energy.

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Uh? The Hamiltonian last I checked is a model of the total sum of Energy in most cases. So not even total sum in all cases. And when it comes to modeling:

As someone with a M.Sc. in "simulations", I have seen how the sausage is made.
Successful simulations are good on the 'this model is useful' scale, but a dead zero on the 'this model has anything to do with reality' scale.

*shudders at the memory of some lectures on turbulence modeling, and schedules another therapist appointment for his sense of math*

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Yeah as @Yla said emulation and simulation are not the same thing and we don't do all that much to actually emulate reality in our calculations. Most of the time it's just the simulation of all the known empirical components which doesn't cover any unknown or unthought of variable/reaction.

From context of the statement of the involvement the Einsteins and 'unifying' Matter and Energy, we're talking about the development of special relativity. From the point of view of STR's fundamental relations, it makes no sense to single out energy, and momentum is equally unified; the OP explained this as well. Furthermore, the symmetry group of of STR is Poincaré, the Casimir operators of which are mass, spin, and parity. So you're simply mistaken about spin, and it's no accident why those are the first ways fundamental particles are classified (the other quantum numbers, e.g. charge and isospin, are 'internal', though).

Finally, both the mode of thought and the weird capitalisation are more reminescent of the XIX/early XX century natural philosophy than physics in the last hundred years.

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I'm talking about Chemistry in a subtly different scientific paradigm from yours. What of it?

What you're saying just doesn't have much to do with anything.

The whole issue of unification of Matter and Energy isn't actual physics strictly speaking, and none of your reference to Noether and Hamilton changes that fact (and is fundamentally wrong regarding spin anyway), especially as they're not even a product of relativity, which was the topic. There are some particles (or fields, if you like), and energy is one of their observable properties, and they have other observables. Matter isn't equivalent nor ever turns into energy strictly (except as a metaphorical description which may be good enough for many purposes); particles turn into other particles.

It is true that in many ways energy has more practical significance than other observables, but it is no more or less 'unified' with matter than a host of other properties.

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Just wanna point out: The original starting point for this particular discussion was QM.

I'm not sure why you think it (what it? Presumably the Noether Theorem) is fundamentally wrong for spin. No, spin is not derived from the Noether Theorem, but I never cited that either, and it does derive from the symmetry of the spin group. Same idea.

Now, what is your definition of matter? From context, I assume @Dmol8 means 'mass'. I don't think you do. Hence, talking past each other.

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Matter is the sum of everything in the universe and Energy and Substance are subsets of it. Energy also doesn't mean just Joules since it is a translation to your system from mine with the original meaning being Physical Fields and not just Force applied to a Distance. Relativity is also not the topic, but a demonstrative example of how the differences between the systems manifest with one side venerating the discovery of the fact that Matter and Energy can be transmuted into one another, while the other started to wonder if the two subsets of Substance and Physical Fields were enough.

Also particles turning into other particles works well enough until you have to ask for an example how does the flip in Quantum Numbers happen in the creation of anti-matter. Or if you take a look at Spin as a concept and realize that it is literally the leftover remains in an old calculation to understand the movements and positioning of an electron.

And while we are on the topic of useful observables how many of the base 7 can you even name?

 

[Vorpal]

Just wanna point out: The original starting point for this particular discussion was QM.

I'm not sure why you state it (what it? Presumably the Noether Theorem) is fundamentally wrong for spin. No, spin is not derived from the Noether Theorem, but I never cited that either, and it does derive from the symmetry of the spin group. Same idea.

Now, what is your definition of matter? From context, I assume @Dmol8 means 'mass'. I don't think you do. Hence, talking past each other.

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You implicitly cited Noether when you started talking about symmetries of physics, e.g. when time translation and conservation energy. I've pointed out that none of what you said in that post is fundamentally changed by relativity (or quantum mechanics, for that matter), so bringing it up regarding merits of relativity and Einstein(s) is kind of off-base. The Hamiltonian insight is basically centuries old, too. So most of your post was not wrong, but it doesn't connect to claims in the posts you're replying to.

Matter is a fuzzy context-dependent word, and personally I don't think its identification with mass is a particularly good one, but I've also interpreted Dmol8 as doing so, because that's how typical discussions about STR go. So I've taken the same interpretation that you did. And to that end, I've said that singling out energy is strange because the relevant special-relativistic insight is m² = E²-p², so it's just as well unified with momentum. This has been essentially pointed out in the OP, too. ... In that straightforward interpretation, there's a quick example of something that's not Matter or Energy and unified by STR: Momentum.

You say that the discussion starting with QM, so ok, let's go to special relativistic quantum mechanics, i.e. field theory on a Minkowski background. There, a particle is an irreducible representation of the Poincaré group, i.e. the symmetry group of STR, plus internal quantum numbers. And the Casimir operators of this group, and hence the generated invariants, are: {mass, spin, parity}. So it's just as valid to say that special relativity, the summarised insight of which is that physics has a Poincaré symmetry, unifies those three properties. ... In that straightforward interpretation, there's a quick example of something that's not Matter or Energy and unified by STR: Spin.

Finally, I've taken a potshot at the whole mode of thought, which again is reminiscent of XIX century philosophers. The more relevant physics at the somewhat deeper level is that you have some fields(/particles), which have some properties, including energy, but also including other ones. Even the credible MOND proponents know this, e.g. by introducing extra fields (TeVeS, etc.) or deforming the Einstein–Hilbert action (f(R) gravity, etc.). Personally I think the f(R) is the one of theoretically nicer class of alternative gravity theories, but it's taken some beating from observations in the last decade, too.

Um because the Pilot Wave Theory already redefines gravity and removes a need for a chunk of both Dark Matter and Energy, but not all of it.
...
So I'm looking forward to when we figure out what MOND's version of Oxygen looks like.

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Okay. If that's an argument for MOND, I guess it's growing even more fringe and irrelevant than I suspected.
(I kid; it's not fair to judge it based on this.)

 

[Dmol8]

@Vorpal what I was implying and what I will say outright is that I think MOND as a theory is today's Physics version of the Phlogiston theory: A theory invested in maintaining the old model of observation/analysis of the world to the point of absurd. I find the Pilot Wave Theory to be much closer to Oxygen theory in this comparison instead of some sort of silver bullet that will remove Quantum Mechanics from the equations.

 

[Vorpal]

Ah, my bad. Then I agree with half your general point, with the primary difference is that I view pilot waves a clear example of phlogiston: a theory invested in keeping a classical worldview for no scientifically pertinent reason, just ideological attachment. So this kind of positive comparison threw me off, but that's another kettle of fish.

I don't think it'd be fruitful to butt heads over that, though, so let me say a few quick random things about more basic things.

Substance refers to any piece of Matter that has a particle and Energy in this context refers to Physical Fields. This includes both Momentum and Spin. In fact Spin is the fourth basic Physical Field any piece of Matter has. The basic Physical Fields are know as Quantum Numbers.

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I don't know if this is a translation issue or chemistry over there is really so disconnected from the wider scientific community in its concepts. Regardless, field theory has been the workhorse of physics for many generations by now, and none of this makes sense from that perspective (nor with chemistry books over here I'm familiar with). Rather, particles are excitation in fields, and none of those properties are themselves fields in the physics sense.

Also particles turning into other particles works well enough until you have to ask for an example how does the flip in Quantum Numbers happen in the creation of anti-matter.

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I genuinely have no idea why you're saying this. Under normal circumstances, the relevant quantities are conserved by such processes (e.g. pair creation), so

Or if you take a look at Spin as a concept and realize that it is literally the leftover remains in an old calculation to understand the movements and positioning of an electron.

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That's very mistaken. Well, it is basically true of how it was first discovered, and it is important to be aware of empirical evidence, but not why it's conceptually there.

Rather, spin exists bit measures angular momentum of a particle. In quantum mechanics, observables are operators, and quantising the usual angular momentum gives operators that form a certain Lie algebra. If you then ask which groups have the same Lie algebra, there is actually a discrete set of possibilities, one of which is SU(2), a double cover of the three-dimensional rotation group SO(3), and which we conventionally label spin-½. There is no a priori reason why electrons have spin ½, but the possibility of particles with this spin is immediate from the rules of quantum mechanics applied to angular momentum. (It's even stronger in relativistic context, where spin forced on us from the Poincaré group, and any spin j=0,1/2,1,3/2,2 is allowed. For some much deeper reasons, spins higher than 2 turn out to be verboten.)

So you have to do at least one experiment to figure out that electrons have spin 1/2. If you theoretical framework generically predicts that fundamental particles have one of four spins, saying that the electron is one of the four is not in any sense a problem.

I think this approach is far more conceptually powerful than some Bohr model-inspired taxonomic catalogue. For example, if you ask about the structure of the hydrogen atom and know that the relevant Coulomb force is inverse-square attractive and electron is spin 1/2, then you can calculate the hydrogen energy levels from the fact that the Kepler problem has an SO(4) symmetry, that the degeneracy is of the energy is n², and that some of the general pattern of the periodic table: the rotation group SO(3) has irreducible representations of each odd-number dimension, and the electron spin group is a double cover of SO(3), so if we imagine filling up a hydrogen-like atom with no electron-electron interactions, they will be filled a double-of-odds pattern (2s,6p,10d,14f, ...). Of course, electron-electron interactions and other various corrections make real atoms more complicated, especially the heavy ones, but we get a big chunk of the structure of the periodic table just from the symmetry considerations.

YMMV, but in physics, it's much more satisfying to understand at least part of a general structure like the periodic table as a consequence of some higher principle, in this case how rotations work, right than a Bohr model-like cookbook. And that comes with treating the conceptual origin of spin seriously.

And while we are on the topic of useful observables how many of the base 7 can you even name?

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Base 7? Pfft. The Eightfold Way is obviously better. (Only slightly more seriously, the best base is obviously e. That's why it's natural and has the best radix economy.)

 

[Dmol8]

I don't know if this is a translation issue or chemistry over there is really so disconnected from the wider scientific community in its concepts. Regardless, field theory has been the workhorse of physics for many generations by now, and none of this makes sense from that perspective (nor with chemistry books over here I'm familiar with). Rather, particles are excitation in fields, and none of those properties are themselves fields in the physics sense.

Click to shrink...

Sigh. I know about field theory. It is used over here as well. It is just not considered the only model. It depends on what you are trying to do with your Chemistry if you will use either Field theory or the old Substance system. The problem is that the Substance system is not an old anachronism kept simply out of nostalgia and academic inertia: We haven't fully figured out how to integrate the two systems by either making the Substance system a special case for the Field theory or by making the Field theory a statistical model for the Substance system. It's why I think the Pilot Wave Theory is like the original Oxygen theory: It brings the possibility of a plausible resolution to this impasse of models in use one way or the other.

I genuinely have no idea why you're saying this. Under normal circumstances, the relevant quantities are conserved by such processes (e.g. pair creation), so

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Wait we're still using pair creation for anti-matter production? Well shit my objection is then senseless.

That's very mistaken. Well, it is basically true of how it was first discovered, and it is important to be aware of empirical evidence, but not why it's conceptually there.

Rather, spin exists bit measures angular momentum of a particle. In quantum mechanics, observables are operators, and quantising the usual angular momentum gives operators that form a certain Lie algebra. If you then ask which groups have the same Lie algebra, there is actually a discrete set of possibilities, one of which is SU(2), a double cover of the three-dimensional rotation group SO(3), and which we conventionally label spin-½. There is no a priori reason why electrons have spin ½, but the possibility of particles with this spin is immediate from the rules of quantum mechanics applied to angular momentum. (It's even stronger in relativistic context, where spin forced on us from the Poincaré group, and any spin j=0,1/2,1,3/2,2 is allowed. For some much deeper reasons, spins higher than 2 turn out to be verboten.)

So you have to do at least one experiment to figure out that electrons have spin 1/2. If you theoretical framework generically predicts that fundamental particles have one of four spins, saying that the electron is one of the four is not in any sense a problem.

I think this approach is far more conceptually powerful than some Bohr model-inspired taxonomic catalogue. For example, if you ask about the structure of the hydrogen atom and know that the relevant Coulomb force is inverse-square attractive and electron is spin 1/2, then you can calculate the hydrogen energy levels from the fact that the Kepler problem has an SO(4) symmetry, that the degeneracy is of the energy is n², and that some of the general pattern of the periodic table: the rotation group SO(3) has irreducible representations of each odd-number dimension, and the electron spin group is a double cover of SO(3), so if we imagine filling up a hydrogen-like atom with no electron-electron interactions, they will be filled a double-of-odds pattern (2s,6p,10d,14f, ...). Of course, electron-electron interactions and other various corrections make real atoms more complicated, especially the heavy ones, but we get a big chunk of the structure of the periodic table just from the symmetry considerations.

YMMV, but in physics, it's much more satisfying to understand at least part of a general structure like the periodic table as a consequence of some higher principle, in this case how rotations work, right than a Bohr model-like cookbook. And that comes with treating the conceptual origin of spin seriously.

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Um Bohr's Number refers to the base energy state a particle finds itself in, the Orbital Number is the particle's momentum, the Magnetic Number determines all the possible paths a particle can take trough a(n) (electro)magnetic field and the Spin Number well does a lot of what you said, but at the same time I disagree with some of it primarily the stuff about how orbitals can be calculated only trough using Spin and constants since some of the constants are just tables of the other three Quantum Numbers calculated into a table of values used in the calculation.

Base 7? Pfft. The Eightfold Way is obviously better. (Only slightly more seriously, the best base is obviously e. That's why it's natural and has the best radix economy.)

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Base Empirical measurements we derive all our other measurements from. That are currently 7 in number.

 

[Vorpal]

I strongly suspect this is some translation problem. I don't think anyone in anglophone chemistry would call electron momentum and spin fields. Maybe associate electrons with a spinor field, but that seems different than the direction you're going.

Offhand, it sound vaguely like just the wave model in different terms. But I don't know. :/

Um Bohr's Number refers to the base energy state a particle finds itself in, the Orbital Number is the particle's momentum, the Magnetic Number determines all the possible paths a particle can take trough a(n) (electro)magnetic field and the Spin Number well does a lot of what you said, ...

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The bulk of the above is that your statement

Or if you take a look at Spin as a concept and realize that it is literally the leftover remains in an old calculation to understand the movements and positioning of an electron.

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is simply completely mistaken. It characterises spin as some ad hoc fudge factor to make models come out right. That is not what spin is as a concept. Rather, spin is an inevitable consequence of an electron being able to carry angular momentum by themselves. And if an electron is an elementary particle, its spin is highly constrained to basically be one of very few possibilities, and they're all allowed. I already gave a rough outline why.

(An interesting question is why the standard model does not have a spin-3/2 elementary particle, even though that's one of the four non-verboten possibilities, but that's another issue.)

... but at the same time I disagree with some of it primarily the stuff about how orbitals can be calculated only trough using Spin and constants since some of the constants are just tables of the other three Quantum Numbers calculated into a table of values used in the calculation.

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I said was that if one understands where spin comes from conceptually, rather than treating as a leftover remains, then using this group-theoretic understanding one can also derive:

1) The energy levels of hydrogen, and that the degeneracy of each must be n².
2) A big chunk of the general structure of the periodic table, specifically the double-of-odds pattern for orbitals (2s,6p,10d,14f,..).​

This is meant to illustrate the conceptual power of understanding the actual origin of spin, rather than treating it as some leftover appendix.

What I did not say was that it is enough to understand the full structure of the periodic table (e.g. this doesn't really derive Aufbauprinzip, or much less it in the full glory), nor that everything about the orbitals of a specific atom can be calculated. I also gave reasons why it's not enough for that: mainly, it ignores increased complexity electron-electron interactions, further relativistic corrections especially relevant for heavy atoms, and many other things.

Base Empirical measurements we derive all our other measurements from. That are currently 7 in number.

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All of that can be reduced to GeVⁿ or something. Not good radix economy.

 

[PhoenixMercurous]

Ah, my bad. Then I agree with half your general point, with the primary difference is that I view pilot waves a clear example of phlogiston: a theory invested in keeping a classical worldview for no scientifically pertinent reason, just ideological attachment. So this kind of positive comparison threw me off, but that's another kettle of fish.

I don't think it'd be fruitful to butt heads over that, though, so let me say a few quick random things about more basic things.


I don't know if this is a translation issue or chemistry over there is really so disconnected from the wider scientific community in its concepts. Regardless, field theory has been the workhorse of physics for many generations by now, and none of this makes sense from that perspective (nor with chemistry books over here I'm familiar with). Rather, particles are excitation in fields, and none of those properties are themselves fields in the physics sense.


I genuinely have no idea why you're saying this. Under normal circumstances, the relevant quantities are conserved by such processes (e.g. pair creation), so


That's very mistaken. Well, it is basically true of how it was first discovered, and it is important to be aware of empirical evidence, but not why it's conceptually there.

Rather, spin exists bit measures angular momentum of a particle. In quantum mechanics, observables are operators, and quantising the usual angular momentum gives operators that form a certain Lie algebra. If you then ask which groups have the same Lie algebra, there is actually a discrete set of possibilities, one of which is SU(2), a double cover of the three-dimensional rotation group SO(3), and which we conventionally label spin-½. There is no a priori reason why electrons have spin ½, but the possibility of particles with this spin is immediate from the rules of quantum mechanics applied to angular momentum. (It's even stronger in relativistic context, where spin forced on us from the Poincaré group, and any spin j=0,1/2,1,3/2,2 is allowed. For some much deeper reasons, spins higher than 2 turn out to be verboten.)

So you have to do at least one experiment to figure out that electrons have spin 1/2. If you theoretical framework generically predicts that fundamental particles have one of four spins, saying that the electron is one of the four is not in any sense a problem.

I think this approach is far more conceptually powerful than some Bohr model-inspired taxonomic catalogue. For example, if you ask about the structure of the hydrogen atom and know that the relevant Coulomb force is inverse-square attractive and electron is spin 1/2, then you can calculate the hydrogen energy levels from the fact that the Kepler problem has an SO(4) symmetry, that the degeneracy is of the energy is n², and that some of the general pattern of the periodic table: the rotation group SO(3) has irreducible representations of each odd-number dimension, and the electron spin group is a double cover of SO(3), so if we imagine filling up a hydrogen-like atom with no electron-electron interactions, they will be filled a double-of-odds pattern (2s,6p,10d,14f, ...). Of course, electron-electron interactions and other various corrections make real atoms more complicated, especially the heavy ones, but we get a big chunk of the structure of the periodic table just from the symmetry considerations.

YMMV, but in physics, it's much more satisfying to understand at least part of a general structure like the periodic table as a consequence of some higher principle, in this case how rotations work, right than a Bohr model-like cookbook. And that comes with treating the conceptual origin of spin seriously.


Base 7? Pfft. The Eightfold Way is obviously better. (Only slightly more seriously, the best base is obviously e. That's why it's natural and has the best radix economy.)

Click to shrink...

Quick question, what convention are you using for symmetry operation (covering operation) groups? I've seen symmetry operations from at least two different perspectives, crystallography and quantum chemistry, but I've never seen notation like "SU(3)" and "SO(4)."

 

[Vorpal]

Quick question, what convention are you using for symmetry operation (covering operation) groups? I've seen symmetry operations from at least two different perspectives, crystallography and quantum chemistry, but I've never seen notation like "SU(3)" and "SO(4)."

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I'm not sure I understand your question; the notation is standard in mathematics and not physics-specific. O(n) is the orthogonal group, the symmetry group of n-dimensional Euclidean space that preserves a fixed point, i.e. without translations. SO(n) is the specifial orthogonal group, i.e. also excluding mirror reflections, and thus is just the rotation in Euclidean n-space.

You can represent O(n) as real orthogonal matrices if you like, RT​R=RRT​ = I, which have determinant ±1, and SO(n) would correspond to those with det R = +1. U(n) is the unitary group, which you can represent as complex unitary matrices, with analogous restriction so SU(n).

For example, SO(3) is the groups of rotation in three dimensions (i.e. symmetry of a 2-sphere). SU(2) is isomorphic to the electron spin group; the usual Pauli matrices are just a standard basis for it. If you take them and multiply by i, then including the identity matrix, you have an algebra isomorphic to the quaternions, which represent the same rotation by two different quaternions. So it's at least intuitive that there's a double cover. Here we do have some notional convention differences between mathematicians and physicists, but I gather that's not what you're asking about.

Anyway, one way to think about it is this: if you think your electron has a conserved angular momentum by itself, then guided by the insight of Noether's theorem, the conserved quantity should correspond to infinitesimal rotations. The infinitesimal limit of the rotation group SO(3) is its Lie algebra so(3). The notation is not important, but something special happens: the Lie algebra of SU(2) is isomorphic to so(3). So the requirement of angular momentum conservation can't distinguish between them: the spin 1/2 group must be a valid possibility.

There's a whole bunch of things that can be said in less handwavy way, and have been done in various textbooks and literature, up to and including that field theory essentially narrows the elementary particle spins to {0,1/2,1,3/2,2}, but I hope this clarified some things. The overall point is that characterising spin as some leftover bit and to imply this is some kind of problem or an ad hoc appendix is just wrong. Spin is there because the electron is spinning. (People that have a problem with this statement, and many do, are stuck in a classical mindset. Quantum-mechanically, to say that a physical thing does or doesn't do something is to at least implicitly make an empirical prediction about a result of some observable. Since an electron has intrinsic angular momentum we can measure, it is spinning.)

Also, that the Kepler problem has symmetry SO(4) is an interesting property of bound Newtonian orbits; the motion of the planet in momentum space corresponds through stereographic projection to motion of a free particle on a sphere in four dimensions. This fact was used to first derive the correct energy levels of hydrogen in 1925, i.e. a year before the Schrödinger equation.