You're somewhat correct — there are basically two known generations of stars, and a third hypothesized one.

The very first generation of stars would have lasted millions to tens of millions of years, were very metal-poor (being composed almost exclusively of hydrogen and helium left over from the big bang) and would almost all have gone supernova early on. None are still around today, and there is only scant evidence that they existed at all. Obtaining better evidence for this first generation of stars is one of the primary missions of the James Webb Space Telescope.

The second generation of stars that formed had a middling metallicity, as they formed from material that included the higher-mass elements formed from the first generation of stars. These were lower in mass on average and lasted much longer, hundreds of millions to billions of years.

Our Sun is a third generation star, which was likely formed from the compression of gas by second-generation stars going supernova. Third-generation stars like our Sun are much lower mass and higher metallicity, and have much longer lives on average.

All that being said, we would have obtained a mix of many elements because our Sun (and most second- and third-generation stars) and solar system were almost certainly formed out of gas clouds that had materials from numerous other exploded stars from both the current and previous generation. The second generation of stars was a lot more diverse than the first generation, and the third generation even moreso, so the diversity of elements that we seen in our solar system today comes from many different kinds of exploded stars in the two most recent generations.

Hope that helps!

I think XKCD said it best:

>Yes, everybody has already had the idea, "maybe there's no dark matter — gravity just works differently on large scales!" It sounds good but doesn't really fit the data.

The bottom line is that, even though we've explored quite a lot of modified-gravity / alternative-cosmology models, none of them have been able to fit all of the data even with some of the wildest and most contrived parameterizations. In basically every case, we can choose parameterizations that work to fit some datasets, but then those same parameterizations then go on to fail miserably at fitting other datasets ... and there just isn't any parameterization that works for them all at the same time, which means none of those models are actually viable as models of cosmology.

On the other hand, not only are dark matter models incredibly simple by comparison, but it is straightforward to parameterize them such that all of the datasets are well-fitted with the same parameterization, and getting to that point doesn't even require any specific model of dark matter — the generic idea of dark matter works so well that there are many different possible models of dark matter that work. It could be sterile neutrinos, or axions, or WIMPs, or light supersymmetric particles, the list goes on and on ...

When an idea works so well and with such simplicity and generality while every other idea explored falls flat on its face no matter how complicated you make it, you just have to take a step back and admit that maybe, just maybe, the simple and general idea is actually the correct one. It's kind of like ... if you're sitting there with pegs of different shapes and you find that the round peg fits the round hole but none of the other pegs fit it, well ...

>The inflation in the first microseconds of universe that was faster than C refers only to space - not any of the matter or energy?

It refers to space, but that expansion of space also impacts the matter/energy occupying that space. This does mean that said matter/energy would have had a higher relative velocity than the speed of light ... however that is not an issue because the speed of light limit is a local law, meaning that two objects which are essentially adjacent to each other and capable of communicating causally must never have a relative velocity higher than the speed of light, and that local law is still respected by inflation. For objects which are separated by some distance and not capable of directly communicating or affecting each other causally during the period of inflation, there would be no actual way to measure or compare their relative speeds — any signals emitted by one object during inflation wouldn't be able to reach the other object until the period of inflation is over, since the distance between the signal and the distant object would also be increasing faster than light. Quoting from Wikipedia here:

>>In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.[32]

This is essentially similar to how the law of conservation of energy is also a local law, meaning that localized, pointlike interactions must always conserve energy, but the total energy of a large volume (such as a region of expanding space) can still yield a change in the total energy within that volume.

>The expandsion of space that continues is only faster than C when added up over large distances?

Yes, that's correct. It's technically a misnomer to say that the rate of expansion is "faster than the speed of light" because the rate of expansion is not even a speed to begin with: it is a rate. It doesn't have the correct dimensions/units to be a speed, so comparing it to the speed of light is comparing apples to oranges. Speeds have units of distance/time, while the rate of expansion of the universe has units of 1/time (like Hertz), which is often more convenient to express as units of distance/time/distance (or a "speed per distance"). The Hubble parameter has a value of about 70 (km/s)/Mpc, which means that a galaxy which is 1 Megaparsec away will have a relative speed of approximately 70 km/s. But a galaxy which is 2 Mpc away will have a relative speed that is twice that (140 km/s), and so on. So the relative speed of an object is proportional to its distance in an expanding spacetime. The more distance that is between the two objects, the greater their relative speed will be. With enough distance between them, the relative speed is greater than that of the speed of light ... but then going back to point #1 above, relative speeds greater than the speed of light is only possible for objects with some substantial distance between them. Regardless of the Hubble parameter's actual value, the relative speed of two objects that are close-by always tends toward zero.

>Why do these theories assume the universe originating from a single tiny point? Would the math or evidence be much different if it had instead all originated from the size of a neutron or even a golf ball for example?

General relativity doesn't assume that the universe originated from a single tiny point, rather it derives this conclusion as a consequence of taking the universe's current state and applying the known laws of gravitational physics backwards deterministically to figure out what its past states must have been. When you take our expanding universe and work backwards, it becomes clear that any two distant objects must have been much closer in the far past ... and that if you go far enough into the past, the distance between them becomes arbitrarily small, reaching zero distance in a finite amount of time (elapsed in reverse).

The math/evidence wouldn't be substantially different, because if you work backwards and ask "how would the universe look if you work backwards in time from when it was the size of a neutron or a golf ball" the answer you get from general relativity is unequivocably "it would have been even smaller in the past, and if you go back just a little further into the past, the distance between all objects becomes exactly zero."

Now, it's worth pointing out that using general relativity to work backwards does result in it becoming non-predictive and giving nonsensical, almost certainly unphysical properties as you get closer and closer to that zero point. As you get that much closer, the universe's energy density also grows without bound, asymptotically approaching infinite density ... and we have very good theoretical reasons to expect that there are undiscovered physical processes in play that would have been very important for the universe's earliest dynamics — for example, corrections to general relativity due to any undiscovered quantum nature of gravity, which might prevent reaching a state where the universe is actually singular, with zero size and infinite density. But until we discover said processes/corrections, understand them, and reconcile them with general relativity's naive classical predictions, we won't be able to properly model the universe's behavior in such a state. So the best we can say at the present time is that general relativity seems to work reliably back far enough in time to where the universe was in an extremely condensed state, but prior to that point, we can't truly be certain just what the earliest moments of the universe were like. All we can say is that the observable universe at one time was in an extremely condensed high-density state, and it expanded from there into what it is today.

Hope that makes sense!

Neat, thank you!

> ... We can consider two regimes which are categorized by the magnetic Reynolds number (Rm). ... In the simple case with low Rm then the field strongly influences the flow but the flow does not strongly influence the field. The high Rm case is more difficult as the field and flow are strongly coupled and Alfvens frozen flux theorem is applicable (which essentially says that the fluid flow is frozen to the magnetic field and vice versa).

Huh ... I'm curious, is there any intermediate regime, however small or poorly-understood it might be, where there is some substantial back-reaction of the flow onto the field but not enough to freeze the fluid flow to the magnetic field ... or is there essentially a hard phase transition between the two behaviors?

Cheers!

>How do we account for red shift without knowing distance?

We don't. We know the distance, at least to within some margin of error that is always accounted for.

>AFAIK the shift itself is the only way we can measure distance at cosmological scales.

That isn't accurate. You probably want to do a little bit of reading into the cosmic distance ladder and how it is constructed. Redshift needs to be accounted for at all but the closest distances, and there are close to two dozen different ways of measuring differently-sized distances that cover overlapping distance ranges, and which are all in general agreement with each other within the overlapping ranges, as well as in agreement with the measured redshifts.

Hope that helps!

>How are we sure [that constants don't vary over space and time]?

Well, we test that hypothesis by looking at measurable quantities which would be different if the constant were different. This is easier to test for some constants than others.

For example, if the fine structure constant were to vary across space, that would have a major impact on chemistry — chemical bonds would have different characteristic energies, light emitted when breaking those bonds would have different wavelengths, and different kinds of bonds would be possible in general. For example, the Lyman-Alpha hydrogen line would have a wavelength different from 121.567 nm. But when we look out into the cosmos, and do spectroscopy of distant stars and galaxies, we see that they all have on average the same composition of frequencies, and the Lyman-Alpha line at 121.567 nm is strongly seen (after accounting for known effects such as redshift of course). So, that's one way we know that the fine structure constant is actually constant throughout the entire observable universe.

Likewise, for the speed of light in particular, one possible test (of many) of the speed of light in distant galaxies comes from type 1a supernovae measurements and something called the cosmic distance duality relation (CDDR), which according to the linked source is model-independent and can only be violated by three conditions (non-Riemannian geometry, which would mean general relativity itself is entirely inapplicable and which seems incredibly implausible given the successes of general relativity at modelling the cosmos as a whole, and similarities in distant measurements of other constants such as the fine-structure constant mentioned above; a source of opaqueness in the cosmos, i.e. some kind of foreground dust blocking our view of distant objects, which obviously isn't the case; and, variation in fundamental physical constants such as the speed of light). By comparing these measurements, they determine that the CDDR is respected even in distant galaxies, indicating that none of those three conditions apply.

And there are a variety of other possible tests as well; off the top of my head I vaguely recall hearing about one involving comparing the delay times of light from a certain supernova to neutrinos that were detected from the same supernova, and I think there was also one involving the delay time of light emitted directly by a supernova versus light emitted by a cloud of gas surrounding the supernova as a consequence of a shockwave, or something along those lines ... though I wasn't able to find references for these in a cursory Google search. I'm sure if you searched around you could find these and/or other methods. (Edit: Also I remembered another detail — since the speed of light is related through Maxwell's equations to the electric permittivity and magnetic permeability of the medium it's travelling in, tests of these two quantities for the vacuum or perhaps even for known kinds of systems like gas clouds surrounding a quasar or supernova in distant systems could also help confirm or refute differences in the speed of light within those systems.)

But suffice to say, the way we know it's the same is by looking at distant systems and seeing that they behave the same as nearby systems, specifically in situations where a different speed of light or other different physical constants should cause them to behave differently. To date, there is no convincing evidence of any discrepancies between the speed of light on Earth and the speed of light in distant galaxies.

Hope that makes sense!

Classical relativity, also known as Galilean relativity, is what you learn in high school; it has simple transformations between different reference frames, where every reference frame is on the same "time" but have different positions and speeds for different objects. And if you want to transform from one reference frame to another, you basically just add all the speeds and displacements, linearly. So if you're changing from frame A to frame B, then the speeds are all V_B = V_A + V_difference, and the positions are all x_B = x_A + x_displacement. It's nice and simple, mathematically.

Galilean relativity is really accurate in most circumstances, but not in all — specifically it becomes less and less accurate the faster you are moving. The experimental discovery of this led to the development of special relativity. Basically, physicists (including Einstein, Lorentz, and Poincaré, among others) realized that the transformation leaving time unchanged was wrong, and that the transformation laws weren't that simple. Lengths had to shorten (length contraction) and durations had to lengthen (time dilation) in order to preserve the speed of light across all reference frames. This makes special relativity a bit more complicated than Galilean relativity (it's no longer just adding speeds and displacements, you have to do multiplication and division of various extra factors now), but fortunately it's not too complicated — you can understand most everything in special relativity with just high school algebra, it's just not neat and linear anymore like Galilean relativity is. This new flavor of relativity was just called "relativity" by Einstein, and today is known as "special relativity" because it is a special case of general relativity.

Here's a really good short video illustrating the difference in reference-frame transformations between special relativity and Galilean relativity.

Not long after special relativity was developed, Einstein was able to further generalize special relativity, which lead to the development of "general relativity." General relativity is basically special relativity, but in curved spacetime (where special relativity only allows for flat spacetime). Because it can handle curved spacetime (and because it expresses a specific relationship between the curvature of spacetime and matter/mass), it can also model gravitational dynamics. Gravity then is not some extra force that needs to act on flat spacetime, it emerges naturally as a fictitious force (or "inertial force") due to the curvature of spacetime. General relativity is substantially more complicated, mathematically, than special relativity is — it involves non-linear partial differential equations, a special kind of abstract geometry called pseudo-Riemannian geometry, etc. But for modelling the most complicated gravitational situations (like black holes, neutron stars, and the cosmos as a whole) it is necessary. Special relativity and Newtonian gravity just don't give the correct answers together. General relativity became famous when it first predicted (or actually, retrodicted) the correct value for the precession of Mercury's orbit and for the deflection of light around the Sun from sources behind it.

Hope that helps!

There isn't a lot, no. Dark matter is very diffuse; in all likelihood there is some streaming through the planet every second of every day, but since it doesn't really interact with baryonic matter much if at all (similar to how neutrinos don't), studying it would be exceedingly difficult. There have been many experiments similar to current neutrino detectors looking for dark matter interactions but none have been found to date.

Uhhh ... it's been happening for basically as long as we've known dark matter existed? The first real evidence for dark matter started coming in almost 100 years ago, in the 1930s and 1940s. The earliest dark matter models were overly simple — just treating galaxies as if they had extra mass — and they had various problems. Throughout the following decades, models of the cosmos became increasingly sophisticated ... and increasingly conflicted, as every model had some seemingly irreconcilable problems (regardless of dark matter) so it wasn't clear which model was the correct, or even the closest to correct. As I understand it, during the early 1980s the first modern models of dark matter were proposed, with distributions not matching those of baryonic matter. And with the discovery of the accelerating expansion of the universe and the need for a cosmological constant or some other form of dark energy, in the late 1980s / early 1990s, enough evidence had come in for cosmologists to hone in on a model that resolved all the issues with the previous competing models — this model is known the Lambda-CDM model (lambda is the symbol for the cosmological constant term in the Einstein field equations, and CDM stands for "cold dark matter"); it is also known as the "concordance model" because it gracefully resolved all the outstanding problems with the previous models of cosmology, and fit the data much better than any of those other models. Since that time, this model has become known as the "standard model of cosmology" and has stood out as effectively the only model that actually works and fits all of the data. Dark matter has been a part of that model since its inception in the early 90s, and in the three decades since all sorts of tweaks, additions, and parameterizations of that model (including its dark matter aspect) have been explored ... as well as many alternative models, none of which have panned out and found success at fitting all of the data well.

So dark matter has been an accepted part of the modern model of cosmology for at least 3 decades and we've had all manners of more complicated models (and attempts at alternative models) developed during that time. All sorts of supercomputing simulations of structure formation in the cosmos have been run and their statistics compared to observational datasets, with gradual refinement of the narrower strokes as new data has come in from missions like WMAP and the Planck spacecraft.

In summary, it's been happening this entire time because that's what cosmologists do — that's their job. It's not like they've been slacking off for half a century; there are tens of thousands of cosmologists and astrophysicists worldwide who have been working on it doing formal research and experimentation/observation for their entire professional careers. :)

>Do you mean a type of dark matter has been observed?

Yes as I explained two posts prior, we have observed dark matter directly — three types of dark matter, in fact: the electron neutrino, muon neutrino, and tau neutrino.

>That doesn't mean this particular observation is the dark matter that is responsible for the differences in our calculations - measurements for galaxies.

Yes, I explained that too, also in the second to previous post. Perhaps you should go back and read it!

The difference is that the Bullet cluster is an observation that needs to be explained for you to have a viable model of the cosmos. Any model which cannot explain it is not viable.

Dark matter models can explain it ... and also can explain all of the other observational data. Dark matter models are viable.

There is no known model of modified gravity that is viable. Every one that has been proposed to date is either too vague to make novel testable predictions (in which case you can't really call it a model to begin with), or it has made novel testable predictions that were found to be in conflict with observations, leading to the proposed model being falsified.

The difference between aether and dark matter is that with aether theories, experiment after experiment showed repeatedly that it didn't exist, or at least didn't work the way it was supposed to. There was Fizeau's experiment in 1851 which largely ruled out any aether drag effects, the Michelson—Morley experiment in 1887 which established the constancy of the speed of light and ruled out the aether wind hypothesis, the Trouton–Noble experiment in 1903, the Rayleigh and Brace experiments between 1902 and 1904, ... there was a wealth of experimental evidence available showing the problems with aether models. Also it wasn't "nearly consensus" that aether existed, there was quite a lot of debate all throughout that period as to whether light was a wave (one that travelled in a presumed medium — an aether of some sort) or whether light was a particle or "corpuscule" (and hence a form of matter that did not require a medium within which to propagate). Various people proposed either/both wave- or particle-based theories of light and experiments continued to both confirm and refute aspects of each proposed model, all the way from their inception into the early 20th century. The problems with both kinds of models only really began to start being resolved with the advent of early quantum mechanics and the emergence of wave-particle duality as a feature in physics.

With the dark matter situation however, you have dozens of kinds of observations that are all in general agreement about dark matter, while those same observations are largely contradicted by the predictions of modified-gravity models. Unlike with the aether, this isn't a situation where nobody's model fits all the data; with dark matter there is a clear matter-based model that does fit all of the data, and then a bunch of alternative models that don't. That's a pretty huge difference.

>I’m far from an expert, and dark matter seems from what you write proven by many independent sources. But, I can guess, for many, it smells like an esoteric substance stubbornly refusing to be directly identified.

And this is the crux of the public relations issue on this topic: really only the people who are "far from experts" who aren't actually familiar with all of the evidence feel that way. Among actual experts, the consensus is that dark matter exists and that modified gravity models don't actually work. The only people who really have a problem with dark matter anymore are the ones who are uninformed about it. :(

Well, if it makes you feel any better, we've also explored every other type of possibility that is allowed:

• scalar field models, like the Higgs field
• vector field models, like electromagnetism and the strong and weak interactions
• tensor field models, like general relativity and modifications of it
• supersymmetric matter models

These, together with ordinary matter models, are exhaustive of what the allowed possibilities are, at least for particle forms of dark matter (keeping in mind that aggregate forms, such as black holes and other MACHOs, have also been largely ruled out except for within a range of very small masses). There are also combinations of these, such as TeVeS (which gets its name from combining tensor, vector, and scalar fields).

To date, the only types of models that have succeeded at explaining all of the observational evidence are matter-based models (and possibly some of the more contrived supersymmetric matter models, I am not super familiar with those but I assume they operate similarly to matter models — what I do know is that the most minimal supersymmetric models have been observationally ruled out and to date there remains zero evidence for supersymmetry in nature ... though not for lack of trying; discovering supersymmetric particles was one of the goals of the LHC, as well as other experiments).

So, it's not so much an assumption, so much as "we've explored all of the other possibilities and this is the only possibility that actually works."

XKCD wrote a comic about this. There seems to be this popular misconception that we just assumed it was matter because that's simple. No, we "assume" it is matter because virtually every other possibility has been heavily explored and every single one of them has failed to fit all the data even in the most contrived circumstances. Dark matter is really the only game in town, it is the only model of all the thousands that have been explored which fits all of the data.

>If we were in space at relative rest ...

At relative rest with respect to what? Remember ... all speeds are relative to other things! :)

>... and there was an earth-mass chunk of dark matter that wandered into our path, ...

Dark matter doesn't really clump up the way ordinary matter does. The only way you would get this is if dark matter happens to be in the form of "MACHOs" (massive compact halo objects) such as black holes, but that hypothesis has almost been completely ruled out except for a range of masses that excludes things anywhere near the Earth's mass. So, this just isn't an actual possibility, I'm afraid!

>... does that mean we would suddenly find ourselves falling toward it for seemingly no reason?

We would feel its gravitational effects, yes. If you had something like an Earth-mass MACHO, it could do things like disrupt orbits, to the extent that something of Earth mass can do so (naturally something like the Sun or Jupiter wouldn't be significantly affected, but smaller planets would).

>I'm assuming we haven't observed dark matter at smaller than galactic scales, but I'm wondering if the current theories and observations allow for smaller amounts as well.

Unfortunately, not really ... at least, not also in grouped clumps that are within a few orders of magnitude of the Earth's mass. You can have smaller amounts if it is very diffuse (like axions or neutrinos or some other particulate form that doesn't interact electromagnetically) but not if it clumps up due to an interaction of some kind.

>Can we run into planet-sized bits of dark matter just like we can run into planet-sized primordial black holes?

That's a hard no, unfortunately. The observational evidence (at least that which I am aware of) excludes as a form of dark matter MACHOs including primordial black holes in the mass range of 10^(-8) Earth masses or higher. [1]

>One of the theories is that we haven't observed a 9th planet in the solar system that's shepherding things because it may actually be a primordial black hole... Could it also be a small bit of dark matter?

It and things like it couldn't be a significant form of dark matter, no. I don't see why it couldn't be a black hole though, whether primordial or otherwise.

Hope that helps,

Thanks, I'm glad you found it helpful. :) Cheers!

That's fine. I was just responding to try and correct some of the misconceptions in what you said — about dark matter never being directly observed (it has), about us not having strong evidence about its location (which we do), about the certainty of statements about dark matter's other properties, etc.

A lot of this info is outlined in encyclopedia articles like Wikipedia's, so it's pretty accessible. We get a lot of boneheads who won't even do that tiny amount of research before insisting that dark matter is some kind of hoax or fudge factor, so apologies if I stomped on your foot there, that wasn't my intention. I was just trying to respond to the things you said and point out that they aren't correct, lest those misconceptions propagate and get even further out of control. :(

>Dark matter has never been directly observed, ...

I'd like to point out here that the known neutrinos qualify as (hot) dark matter, and other than their very light mass / relativistic speeds, they have essentially identical properties to the cold dark matter that we haven't yet directly observed. So from a definitions standpoint, we have in fact directly observed a form of dark matter (and we regularly produce it in labs for the purpose of studying it). The reason I mention this fact is because people seem to have a common misconception that dark matter is some kind of farfetched, esoteric hypothesis that makes it different from everything that we actually do know, when the reality is that it's incredibly similar to some of the things that we do already definitely know — so similar in fact that one of the leading hypotheses for a cold dark matter particle candidate is in fact a heavy neutrino.

>... to my knowledge there isn't even strong evidence of where its located. So the certainty of statements like "dark matter has no coherent motion" I think needs some caveats.

I'd now also like to point out just how overwhelming the evidence for dark matter is. Contrary to what you've said, we do in fact have multiple ways to measure the bulk properties and behavior of dark matter with enough sensitivity to narrow in on its locations, densities, velocity distribution, speed distribution, etc. This sort of evidence comes from about a dozen completely independent metrics:

• Galaxy rotation curves
• Velocity dispersions of stars in galaxies
• Gravitational lensing and microlensing surveys
• X-ray spectra from gas-heavy galaxy clusters
• The angular power spectrum of the CMB
• The matter power spectrum and rates of structure formation in the early universe
• Observations of more than a dozen colliding galaxy clusters, including the Bullet Cluster, Abell 520, NGC 1052-DF2, and many others
• Reconciling type Ia supernova distance measurements with the observed flatness of the universe's shape
• Galaxy redshift surveys
• Spectral measurements of the Lyman-Alpha forest for distant galaxies

... and there are even more things not mentioned in this list as well. What really drives the nail home is that all of these completely independent metrics are all in close agreement as to exactly how much dark matter there is, how it is distributed, and what most all of its bulk properties and behavior are. When you have such a wealth of evidence where all of it is unequivocably pointing toward the same explanation ... there's just no reasonable excuse to deny it.

It may be true that we haven't directly detected individual cold dark matter particles, but that doesn't mean we haven't detected the direct consequences of the existence of cold dark matter in bulk. The various observational signals supporting the existence of cold dark matter are clear, robust, and all consistent with each other. Among honest researchers as well as honest laypeople who have an interest in science, there really can be no doubt that dark matter exists and has all of the properties that we've undisputably discovered it to have.

Edit: think about it like this. Many hundreds of years ago, people didn't know what the mechanism underlying fire was. Some people postulated the existence of a light, flammable fluid inside most forms of matter called phlogiston; others sought out different alchemic explanations. At the time, nobody knew what fire actually was at a microscopic level; they didn't know about oxygen, combusion, or chemistry in general. But do you think anybody working on the problem at the time would have denied the existence of fire? Of course not — all you had to do was rub some sticks together to prove that fire clearly existed! You don't need to have a microscopic understanding of fire in order to know with certainty that fire exists, because you can clearly see the bulk behavior of fire with your own eyes. The situation is similar with dark matter, today: we may not know what its microscopic description is yet, but we can see the macroscopic evidence very clearly with our various telescopes and instruments that are designed for making precision measurements of the cosmos. The evidence we see for dark matter's existence is quite clear and undeniable.

>I'd like to say thank you for answering my question!

You're most welcome! :)

>I do have one follow up one though; if these particles are created "out of thin air" and contain mass, where does the mass come from?

From the energy of the particles that go into the interaction. Surely you've heard about Einstein's famous relation, E=mc^(2), yes? A given amount of mass is equivalent to a corresponding amount of energy, and vice-versa. So, if you have enough energy, you can create particles with up to however much mass corresponds to that much energy.

>The Law of Conservation of Mass states that particles cannot be created.

No, it doesn't, because there is no law of conservation of mass. There is only conservation of energy.

Mass is approximately conserved in chemical interactions, but even in chemical interactions there are small variations in mass for most interactions because of effects like binding energy and the mass defect, or the release of energy in exothermic reactions.

But either way, there really is no such thing as a "law of conservation of mass," and even if there was, such a law would only say that mass is conserved, it would not say anything about particles not being allowed to be created. Remember: mass and particles are different things. Particles are real physical entities; mass is just a numeric property that particles have, like energy, electric charge, or velocity. Mass is not some kind of physical, tangible thing. It's just a number — one that is involved in governing the behavior of objects which have it.

Hope that helps clarify,

Eh, it's ... both right in a sense, and wrong in a sense, to say that particles can be created out of energy.

Energy isn't a thing — it has no tangible, corporeal existence. It's not itself a particle, or a constituent of any system — for a given system, there's no part that you can point to and say "that's the energy, right there." Rather, energy is a number ... a property of the system, part of the physical description of a system (or in other words, "physical information"). Now, it's a very important number, since it is conserved in local interactions and that conservation law puts constraints on what is allowed to happen. But it's not itself a physical thing; it is a concept, and a fairly abstract one at that (you can't even directly measure energy, it always has to be calculated from other measurable properties such as mass, force, velocity, etc.). So it's not really correct to say that anything is "made up of" or "created out of" energy. What is correct is to say that systems have energy.

On the other hand, since energy is a property of systems, in order to create a physical thing, you need to imbue it with the necessary amount of energy, which has to come from some other system or process.

For example, in the process of annihilation, a particle and antiparticle collide and destroy each other. However, energy is required to be conserved, so they can't just both be destroyed and that's the end of the process, because then what would conserve the energy? So as a consequence of the law of conservation of energy, new particles must be created in order to carry that energy and conserve it.

So in that sense, you do need energy to create particles. They aren't "made up" of the energy, but they do have the energy that is carried over into them, and some energy is required to create particles (at a minimum, at least as much energy is required as the particle would have due to its rest mass).

Anyway, to get a bit closer to your main question about Matt Strassler's quote, the bottom line is that nature obeys what Murray Gell-Mann called the totalitarian principle: "that which is not forbidden is compulsory." Meaning, that if a hypothetical process is not forbidden, then it will/must eventually occur (unless something else that is not forbidden happens first). Or more accurately, if it is not forbidden, then it contributes to the path integral, and has some probability to occur within a given period of time.

So, this begs the question: what determines whether a process is forbidden or not? And the answer is: conservation laws. A process is forbidden if it would violate a relevant conservation law; otherwise, it is allowed. Any process you can think of, as long as all the conserved quantities balance out at the end of the day, that process is allowed, and has some probability to occur!

Now, for most systems, conservation of energy acts as a very big limiter on the allowed possibilities, which is why it's such an important and ubiquitous conservation law. For example, something like an electron can't just turn into a muon, because muons have a higher mass (and a higher associated energy), so you could only turn an electron into a muon if you also gave it enough energy to make up the difference in mass.

And essentially, that is what we do in high-energy particle colliders. By colliding particles together at extremely high speeds (where they have many, many times more kinetic energy than they have mass-energy), we can make them interact with each other while having a huge abundance of extra energy available. Because that energy is available, new particles can be created and processes which would create particles out of "thin air" can proceed, since there is enough extra energy available to satisfy the law of conservation of energy. If there is a lot of extra energy (which there is, in modern high-energy colliders), then even particles which have a really large mass can be created while still satisfying the law of conservation of energy.

And so, in particle colliders, there is so much energy available that lots of brand new particles can be created, including rare ones with very high masses such as the Higgs boson, or the top quark.

And that's essentially what is described by Strassler's quote. By colliding particles together and making them interact at high energies, they are allowed to interact in ways that create brand new particles using some of the available energy. They are allowed to interact this way because, with so much energy available, nothing forbids it anymore — all the conservation laws get balanced out and conserved, including the law of conservation of energy. If a conservation law might forbid it (such as conservation of electric charge), and there is enough energy available to create yet another particle to satisfy the conservation law, then multiple particles may be created — however many are needed to satisfy all the conservation laws. Or even more than are necessary; so long as the laws all are satisfied, it is allowed to happen, and will happen with some probability.

Hope that helps explain it! Cheers,

>Well it comes to the theories themselves I understand they have certain eV ranges. Are these ranges gigantic ?

The gap between the electroweak and GUT scales is pretty gigantic. As for theories of new physics between them, it depends on the theory. Some have narrower constraints on their possible ranges than others.

>It still seems to suggest that the possible eV Range of detections of what I assume is either branes or some kind of extra dimensions goes all the way from 3TeV which is what apparently we have checked so far goes possibly up to the GUT scale itself.

Yes, my understanding is that colliders like the LHC can only raise the lower limit on the energy scale (or equivalently, lower the upper limit on the length scale) at which any small extra dimensions could become apparent, but since there isn't really any way to place an upper limit I am aware of, the range of possibilities is quite large.

>Does that mean unless we build some kind of Gigantic particle collider that is somehow the distance of Earth to Mars. We may very well never reach these scales for possibly centuries?

Essentially, yes. We can keep making incremental improvements — perhaps even a few substantial leaps — but speaking frankly a lot of the hypothetical higher-energy phenomena that is closer to the GUT scale are likely to be practically inaccessible to us for ... well, probably more than just centuries. Personally I place the likelihood that human civilization peaks and wanes to be greater than the likelihood that we ever make it far enough to test any physics that might lie near the GUT scale.

>Can you observe certain phenomenon at those scales with telescopes from some mechanism.

Only if you can find a natural system out there in the cosmos which both exhibits those phenomena and is observable with a telescope. Some important high-energy phenomena, such as those at the surface of a neutron star, might become observable (but also with some very dramatic improvements in telescope capacities). But it's not like we could point a telescope and see things like individual particles out there in space, especially not high-energy particles that nearly instantly decay after being produced. That might happen in, say, a supernova event, but imagining the feat of engineering it would take to make such tiny and precise measurements in the vicinity of a supernova without being obliterated ... it's probably much simpler to just create any such particles in a laboratory on or near Earth, even if it does take up such an enormous amount of energy to access.

>I’m sorry if I’m asking a billion questions this stuff is just amazing to me.

Nah, no worries, it is good that you are curious! :) You are asking good and thoughtful questions; keep 'em coming if you like!

Cheers,

With some exceptions for certain kinds of hypothetical phenomena, where we have reason to expect a certain energy scale or range of energy scales (like how we expected to find the W and Z bosons around the scale of the Fermi constant, roughly 100 GeV), it seems to be generally considered unlikely.

High-energy particle physicists often consider what is known as the [desert](https://en.wikipedia.org/wiki/Desert_(particle_physics)), which is a large gap in energy scales between the electroweak and strong scales where no significant new physics is anticipated to be found.

There are some valid reasons to be skeptical about whether there is such a desert though, of course, and there are certain classes of hypothetical phenomena that are proposed to lie within the desert, such as heavy superpartners to each of the known particles if supersymmetry exists but is spontaneously broken in nature, or heavy sterile neutrinos if right-handed neutrinos exist and there is a see-saw mechanism that drives the right-handed neutrinos to have very heavy masses while driving the left-handed neutrinos to have very light masses.