© Matt Strassler [April 13, 2015]
Dark matter — more elusive than your missing car keys, and more mysterious than that funny light on your dashboard. It probably exists, and if it does, it makes up most of the matter in the universe. It may be made from particles, and if so, and if scientists are lucky, the Large Hadron Collider [LHC] may actually be making a few of these particles. Well, whether they’re making dark matter or not, the LHC experimenters can look for it. (Though they might have an easier time finding your car keys.)
In this article, I’ll try to answer some obvious questions about how LHC scientists could observe effects of a new undetectable particle, and how they could try to obtain evidence that this new particle is actually the dark matter of the universe.
- Detective: “Is there any other point to which you would wish to draw my attention?”
- Sherlock Holmes: “To the curious incident of the dog in the night-time.”
- Detective: “The dog did nothing in the night-time.”
- Sherlock Holmes: “That was the curious incident.” [A.C. Doyle]
How Can LHC Experiments Detect the Undetectable?
The LHC experiments ATLAS and CMS can indeed search for dark matter. This isn’t like looking for your keys, though, because ATLAS and CMS have no hope at all of detecting dark matter directly. But then again, neither experiment detects neutrinos directly either!
Neutrinos, which LHC’s proton-proton collisions produce many times a second, go right through ATLAS and CMS without hitting anything, and leave no trace. Despite this, ATLAS and CMS can and do still infer that neutrinos have probably been produced, and they can use the same technique for dark matter. I’ll describe that technique now; it’s pretty simple. In the following sections I’ll explain how one might hope to distinguish dark matter from neutrinos; that’s much more subtle.
[Note: when I say “undetectable” in this article, I specifically mean “undetectable by the LHC experiments.” Neutrinos are undetectable at the LHC, but they can be detected, with great difficulty and with very low probability, in experiments of a very different type. These tend to be very large experiments, involving, say, huge water tanks, and in some cases they may only detect a few neutrinos a month! The situation with dark matter may be similar; numerous experiments are counting on it.]
The basic principle that underlies the technique is known as “momentum conservation”. This is easily illustrated, if you’re sufficiently clumsy. Take a glass of water, and pour it suddenly, and straight down, onto the floor of your shower. A splash results. Notice (Figure 1a) that the water goes in all directions, leaving a roughly circular pattern on the floor. The important phrase is “in all directions”. You won’t ever see all of the water splashing to the left, with none of it splashing to the right. Well, this is a consequence of momentum conservation, and that principle governs the trick I’m about to describe.
There are many other examples where momentum conservation plays a central role, and a few are shown in Figure 1b-1e. An exploding firework makes a symmetric pattern, with pieces flying up and down, right and left, forward and back. Those of you who have fired a gun know that when the bullet goes out forward, the gun recoils backward, and you need to have a firm hold on it or it will go flying. Here’s a video showing an example of this. A jet plane accelerates to high speed by using jet engines that push heated air out the back. Similarly, a rocket is launched upward by directing its hot exhaust downward. The details of the momentum and its conservation are slightly different (and sometimes subtle) in each case, but the underlying principle, and the basic intuition, is the same.
Here’s something you can try yourself (Figure 2). Blow up a balloon, but then aim the nozzle at your face and let go of it. The balloon will go whizzing across the room away from you. Why? Because the air is rushing out of the balloon toward you — as you can feel on your face. But your friend watching this from across the room can’t feel the air, nor can s/he see it moving since it is invisible. Still, because your friend knows about momentum conservation, s/he can infer the air must be moving out of the balloon toward you; that’s the only way that the initially stationary balloon could have begun moving away from you when you released it. This possibility of inferring the presence of something you cannot see, or detect in any other way, is the key idea.
A collision of two protons at the Large Hadron Collider is a little bit like the splash of water in your shower, rotated to make vertical into horizontal. The collision is head-on in one direction — let’s call that the “beam direction”, which is left-right in Figure 3. Let’s call the other directions, namely up-down and toward-away-from-you, the “transverse directions” — transverse, or perpendicular, to the beam direction.
After the collision, dozens of particles (other hadrons created with the energy of the collision) go flying, most of them in roughly the beam direction. We don’t care much about them; they are hard to measure and they are not usually interesting for questions that particle physicists are interested in nowadays. There are also some particles that don’t carry much momentum at all — and we don’t care much about them either.
But sometimes some particles go flying in the transverse directions, with a lot of momentum — we say that they have a lot of “transverse momentum”. Well, momentum conservation says that since the initial protons had no transverse momentum at all, the transverse momentum of all particles after the collision has to balance. If one particle goes up, there have to be one or more particles going downward. If there are particles going toward you, there must be particles going away from you too.
A classic example of a collision of this type is shown in Figure 4. A proton-proton collision occurred in the center of the ATLAS detector, and the particles that were produced and went flying outward were detected, and their tracks measured. Then these tracks were drawn (by a computer) in this figure, to show scientists where they went. Most of the particles went right or left and aren’t even shown. The blue tracks indicate the trajectories of particles that carried very low momentum, so we don’t care about them. But the two yellow tracks that end in a yellow splotch are particles with large amounts of energy and momentum. One of them is an electron, heading upward in the picture. And before we even look for a second particle with large transverse momentum, we already know, from momentum conservation, that there must be at least one particle going down with large transverse momentum. And there is! It’s the yellow track at the bottom, which happens to be an anti-electron, or “positron” for short.
But in Figure 5, you can see another collision, from the CMS experiment. This one has an electron going up, as in Figure 4. But there’s no particle with large transverse momentum going down. What’s happening here?
Well, the most likely possibility is that there really was a particle going down, but the CMS experiment was unable to detect it. Since scientists already know that
- neutrinos and anti-neutrinos are not detected at CMS, and
- electrons and anti-neutrinos are often produced together, in the decay of a W particle,
it is natural to assume that this is what we are seeing here: an upward-going electron that CMS detected, and a recoiling anti-neutrino, moving down, that CMS did not detect.
Of course, one could wonder if momentum might not be conserved. To see why this is profoundly unlikely, we would have to look at a much wider set of experiments over decades, including but not limited to many other measurements made at ATLAS and CMS, to see all the evidence in favor of momentum conservation. To discuss this would be a long article all its own, so let’s set that aside.
Up to this point, I’ve been schematic and qualitative, but it’s important to realize that physicists can make precise quantitative statements about momentum conservation. One such statement is this: if you know that the momentum in the transverse directions is initially zero before a collision, then when you look at the final particles, take each one’s momentum in the transverse directions, and add these transverse momenta all together (as vectors), the sum, which is the total transverse momentum, must be zero.
Specifically, in a proton-proton collision, the momentum of two protons in the directions transverse to the beam direction — the “transverse momentum” — is zero. After the collision at ATLAS, the experiment measures all the particles that it can observe. Some particles go in the beam direction and aren’t measured, but those have no transverse momentum; all their momentum is in the beam direction. Others have small transverse momentum — too small to matter. But one or more may have large transverse momentum. If we add up their transverse momentum and the sum is zero [or rather, if the sum is close to zero — because no measurement is perfect], we can conclude that ATLAS probably succeeded in detecting all of the particles that had large transverse momentum. However, if the sum is far from zero, then we can conclude that ATLAS failed to detect one or more particles with large transverse momentum. Such particles could be of a known type — neutrinos — or of an unknown type, such as (but not limited to) dark matter.
So now you know that if dark matter particles are produced at an ATLAS or CMS proton-proton collision, the experiments won’t actually detect them. But still, the experimenters will be able to infer, from the fact that the transverse momentum of the detected particles doesn’t add to zero, that one or more undetectable particles of some kind were produced.
Of course, the same thing happens if neutrinos are produced by ATLAS and CMS — and that happens many times per second. So how could LHC experimenters possibly figure out that they had made something other than neutrinos? And how could they figure out that this new thing is dark matter?
I’ll address the first question in the next section, and the second question in the section after that.
How Can the LHC Experiments Distinguish Dark Matter From Neutrinos?
The previous section explained how ATLAS or CMS experimentalists can infer that one of their proton-proton collisions has produced one or more particles that passed through the experiment without being detected. But how can the experimenters know whether they have produced something new and potentially exciting, such as particles that might make up dark matter, rather than just neutrinos, which are familiar particles that we’ve known about for many decades now? Why not just round up the usual suspects, instead of declaring that there’s a new criminal in town?
The simple answer is that there isn’t a way to tell, in any one collision, what type of undetectable particles have been produced. There’s also typically no way to tell how many of them have been produced. Instead, information has to be obtained from the patterns seen over many collisions. Specifically, knowledge comes from comparing those patterns to the predictions of the equations used to describe the known particles and forces, equations called “the Standard Model”. What I’m going to do next is give you a one example of how this is done.
The simplest case to imagine is that two neutrinos, or two dark matter particles, or two of something undetectable, are produced in a proton-proton collision. Suppose (Figure 6) that these two particles are the only ones that have large transverse momentum (recall that there are always lots of hadrons produced in a proton-proton collision, but these mainly go in the beam direction and have very low transverse momentum). Well, then there would be nothing to see! For instance, one of these particles might go up and the other might go down, with equal and opposite transverse momentum — just like the electron and positron in Figure 4. But if both of them are undetected, transverse momentum of the detected particles will still appear to balance, and we won’t have any idea that the undetected particles were produced at all!
But all is not lost. It’s a general feature of proton-proton collisions that when any particles, of any type, are produced at high transverse momentum, stray high-energy gluons are produced in the process too. Occasionally one (or more) of these gluons itself goes off into the transverse directions, and therefore has high transverse momentum. In this case we’ll see something similar to Figure 7. This is called a “mono-jet event”, in which one sees a high transverse momentum jet (a spray of hadrons created by the gluon, see here for details of how this happens) recoiling against “nothing”, presumably an unseen neutrino and anti-neutrino (from a decaying Z particle). Compare Figure 7 to Figure 6; now we have a jet with high transverse momentum, while the two undetected particles will recoil against this jet. Since we do observe the jet, we’ll conclude that transverse momentum of the observed particles doesn’t balance, and undetected particles of some type were produced.
In Figure 8 is the same collision as in Figure 7, viewed “end-on”, that is, looking down the beam direction toward the collision point.
Now here’s an example of a real monojet event observed at ATLAS, viewed end-on as in Figure 8.
The Standard Model allows us to predict, with pretty good precision, the fraction of proton-proton collisions that will produce a certain amount of missing transverse momentum. This is shown in Figure 10. The top of the light blue region represents the prediction of the Standard Model for the rate at which neutrinos will be produced with at least one jet (which has several components, shown as different colors; the light blue region represents the largest effect, arising from Z particles that produce neutrino/anti-neutrino pairs). The data are the black points, with uncertainties given by the vertical bars.
The dashed red curve is the sort of thing that one might expect instead if extra dimensional gravitons of a certain type were being produced. The data clearly agree with the Standard Model prediction, and rule out this type of extra dimensional graviton. The data also disagree (though it is harder to tell from the figure) with the effect of dark matter production (for a particular dark matter particle mass and interaction strength), shown in the solid blue curve. If such dark matter were being produced, it would have made the last two or three data points significantly higher.
In this example (and I could give you many others) you see the power of having the Standard Model’s equations to predict the properties of the known particles. It allows us to determine how often we expect to see a single jet recoiling against “nothing”, i.e. against undetected neutrinos. This prediction will match the data if there are no other types of undetected particles being produced by the LHC’s collisions. We expect this prediction to fail only if the LHC is producing a new type of undetected particle, and/or if the LHC is producing neutrinos in an unexpected way, probably in the decay of a new type of unstable particle.
This is a general strategy. We have many predictions, and many measurements, in which we check the distribution of missing transverse momentum within large groups of collisions with similar features. If we see any of these predictions fail, then some process is happening that is not explained by the Standard Model, producing either unknown undetectable particles, or known ones (neutrinos) in an unexpected way.
Such a discovery would certainly be enough for showing the Standard Model does not describe all of the physics at the LHC, and would lead to many prizes for the experimental physicists. But the interpretation of the discovery would be highly ambiguous! Even if dark matter particles were being produced, it wouldn’t be obvious at all! All we would know is there is some process generating undetected particles unexpectedly often. It would be a huge and unjustified logical leap to conclude that the undetected particles were dark matter particles!
How could scientists distinguish the various possibilities and eventually conclude that dark matter had been discovered? Well, it would not be simple and might take many years… decades, even. I’ll address this in just a moment.
Two More Examples
(Here’s where I left off last week…)
Before I do this, though, let me give you two other examples of how dark matter, or other undetectable particles, might show up. The newly discovered Higgs particle might sometimes decay (i.e. disintegrate) to dark matter, or to something else undetectable. Such so-called “invisible” decays of the Higgs are very rare in the Standard Model, so if they are found to be common, that would represent a profound discovery! Searches for such decays are already underway. The invisibly decaying Higgs can’t be observed directly, but the Higgs is often made with W particles, Z particles, or distinctive quark pairs (which give distinctive jets relatively near the beams, Figure 11). These can be observed, along with missing transverse momentum from the Higgs itself as it decays to undetectable particles. However, as usual, there is a similar signal from the Standard Model — where a Z particle decaying to neutrinos takes the place of a Higgs particle decaying to dark matter. The two can only be distinguished by counting how many collisions of this type are observed, and checking whether the number is significantly more than predicted in the Standard Model.
Another example: In many speculative ideas about particle physics that theorists have considered over the years, including but by no means limited to supersymmetry, the equations predict a new electrically charged particle that can decay to dark matter. In this circumstance it is not so unusual for proton-proton collisions to produce an electron (or a muon) and an anti-electron (or anti-muon), plus two dark matter particles that go undetected and provide missing transverse momentum (Figure 12).
The only problem is that the known particles can make something that looks just like this. When collisions produce a positively charged W particle and its anti-particle, a negatively charged W particle, the W’s can decay to something that looks identical to Figure 12, except that instead of dark matter particles, a neutrino and an anti-neutrino are produced. The only way to discover dark matter in this case is to count; if there are new particles as well as W’s, there will be more collisions of this type than expected. Interestingly, there are more collisions than expected in LHC’s current data… not so many that we should get excited yet, but enough that we should watch this closely as the LHC begins to collect another big batch of data.
The examples I’ve described are just three among many. There are more ideas about what dark matter could be than there are dark matter experts, and in each case there may be a wide variety of ways that dark matter might be created at the LHC. We therefore can’t be sure how the experimenters should look for it — so they are preparing a broad-minded, diverse program of searches to make sure they aren’t missing an opportunity.
Even If LHC Discovers New Undetectable Particles, Are They Really Dark Matter Particles?
How can the LHC experiments prove that they have produced dark matter? They can’t… not alone, anyway. Even if they have made a new type of undetectable particle, they will have to partner with at least one other experiment that can directly check whether the dark matter itself — the stuff found abundantly in the universe — is actually made from LHC’s new particles. Simply knowing that the type of particle exists doesn’t prove that it makes up most of the matter in the universe. Just like neutrinos, it might make up only a small amount of the matter in the universe. Or it might even make up none, if the new particles are unstable (as is the case for most types of particles), and have a lifetime long enough to travel out of the LHC detectors unseen before they decay, but short enough that they disappeared from the universe shortly after the Big Bang.
To say it more succinctly: even if the LHC makes and discovers a new class of undetectable particles, there’s no way for LHC experimenters to figure out how many of these particles, if any, remain in the universe today. The LHC is the wrong machine for that purpose.
So what’s to be done? Well, the LHC can be used to figure out some of the properties of the new particles, subject to some assumptions (which can be tested later.) For instance, in the previous section I gave you three examples (and there are many more) of how new undetectable particles could be discovered. In each case, the new particles were produced in a distinct and distinctive way, and other particles accompanied them that gave an indication as to how they were produced. For instance, if the new particles were produced alone, discovery occurred in collisions that made a single recoiling jet (Figure 8). If they were produced in Higgs decays, discovery could occur in events with two high-energy jets from two distinctive quarks (Figure 11). If they were produced in the decay of a new charged particle, discovery could occur (Figure 12) in events with a charged lepton and a charged anti-lepton (charged lepton = electron, muon or tau.) So by looking at what accompanies the new particles, and going even deeper into the details of how much missing transverse momentum is typically produced, scientists can potentially begin to put together one or more hypotheses regarding the nature of these new particles. Those hypotheses will be put into the form of equations, which can be used to make predictions.
Now we’re almost there. If you have a hypothesis for what the new particle might be, you can ask, how would dark matter of the universe behave if it was made from particles of this type?
Specifically, you would ask: precisely how rarely would these particles interact with ordinary matter? and how much energy would they typically leave behind when they do interact? Knowing how much dark matter there is in the universe, you could predict how often existing underground experiments, such as LUX, XENON100, CDMS, etc., would see signals from this type of dark matter. Perhaps the rate is so large that the hypothesis is already invalidated? Or perhaps it is too small to have seen yet, but large enough to see soon?
The other question you would ask is: What would happen if these dark matter particles encountered each other in the center of our galaxy, or in the centers of nearby dwarf galaxies? In these encounters, could they annihilate one another, and produce visible particles, such as electrons, anti-electrons, anti-protons, or photons (particles of light, probably in the form of gamma rays or X-rays)? And you would ask whether existing satellites and telescopes looking for such signals, such as PAMELA, FERMI-LAT, AMS, etc., would have already detected these effects, or whether they could they do so soon.
Only if and when we get enough information from the LHC (or future particle colliders) to formulate clear hypotheses for how the new particles might behave, and obtain clear predictions for what is expected in other experiments, and only if one of those other experiments clearly confirms at least one of these predictions, can we start to talk seriously about dark matter having been discovered at the LHC.
Could this happen, and could it happen soon? Sure. But as you can tell, it requires several fortunate things to happen in a row, so while it’s not impossible, don’t hold your breath. More likely, if it happens, it will take quite a while, perhaps decades. And if dark matter is made of particles that LHC can’t produce, or isn’t made of particles at all, or simply doesn’t exist — well, LHC won’t tell us that. It will simply remain silent on the matter. So we’re hopeful, and they’ll search, but many other approaches toward solving the great puzzles of the universe also need to be pursued.
119 thoughts on “Searching for Dark Matter at the LHC”
Could the density of dark matter particles be high enough to imply there are free dark matter particles floating around inside the “vacuum” inside the LHC. So then could perhaps a different type of dark matter particle created by proton-proton collision interact with these free floating dark matter particles and then be directly detectable ?
No. Not even close. Not even close to close.
If dark matter is not a particle, could it be an as yet undiscoverd or not understood property of space itself?
Dark matter could mainly be made of black holes with a particular range of sizes, clumps of some new material, or something even more bizarre.
But if it is something about space itself, I would say that that effect isn’t what we would call dark matter. Rather, it’s an alternative explanation for what we observe.
However, at some point this answer could devolve into a discussion about semantics. The only interesting thing, in the end, is explaining what we see, not precisely what we call it.
Thanks, Matt, for your earlier reply to my question. Your final sentence said:
However, at some point this answer could devolve into a discussion about semantics. The only interesting thing, in the end, is explaining what we see, not precisely what we call it.
That was really the point of my question. Is there another interpretation of what we are seeing that does not involve dark matter as a particle or gravity as we know it? Could there be an alternative explanation that we just aren’t considering? e.g. as an as yet undiscovered property of space?
Until someone has a definite proposal, with a set of equations we can analyze, I’m afraid there’s not really anything we can discuss.
Thanks for the explanations. With regard to whether or not dark matter is a phenomena of space itself– the vacuum, the following may be helpful. The energy and momentum contained in the particles, including the dark particles, is responsible for the curvature of the 4d space(gravitation). Measurement(WMAP) indicates that space w/o particles is essentially flat, so that the energy/momentum contained in space(cosmological constant) does not contribute gravitationally and that gravitational contribution to observations is how dark matter is “known”. Dark energy is contribution of vacuum energy that results in expansion of the universe or the development of “less curvature”.
Hmm. I think this would need to be written more efficiently to be clear; it’s something I should try to do.
I have no problem with its content, except that if you’re trying to explain this to people who are considering that Einstein’s theory of relativity might not be correct, it’s not obvious this would be what they want to know.
Hawaii Institute of Unified Physics, hiup.org has a theory with equations that explains this.
‘Ether and the Theory of Relativity by Albert Einstein’
“Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance – we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics – if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium.”
if, in fact nothing else whatever were observable than the shape of the space occupied by the dark matter as it varies in time, we should have no ground for the assumption that dark matter consists of movable particles. But all the same we could characterise it as a medium having mass which is displaced by the particles of matter which exist in it and move through it.
If you read the words of a genius, but you don’t understand them, he has done you no good.
It is not for you to tell me I am not doing physics.
Professor, why you feel hurt. Basic science is what Nature does – Does not, which Job, position or Car of a person who predict that.
Sheep people forget who (like Galileo Galeli) said that – but not, what is said.
Sheep people laughed at Galileo, now laugh, if anybody said, Nature does Geocentrism.
Matt’s comment is perfectly valid, he is most certainly “doing physics”, and his explanations here are absolutely consistent with physics. Eventually, some points he makes may be found to be faulty, but that is because nobody as yet knows everything about physics, or for that matter, anything else. It is perfectly correct to question any of his statements or of any current position in physics for as Galileo noted in Il Dialogo, if the statement is found to be true, the questioner learns something, whereas if there is uncertainty, it may open new possibilities. It is not, however, valid to criticise the person. As far as I am concerned, Matt is doing a quite remarkable job in introducing advanced physics to the public at large, and at the very least, he deserves our thanks. So, Matt, thanks.
We repeat it lanmiller.
“CONSERVATION OF MOMENTUM between monojet and DARK particle”
If photon increase its energy (and thus more speed) for a SHORT period – there will be no Electromagnetic radiation (Dark).
If “c” is constant, there should be more “space” – a PHASE change.
The universe is a fractal according to inflation. This fractal-ness is amplified to the current filamentous fractal structure of galaxies and dark-matter distribution.
As the spaces over which particles appear get smaller and the time periods get shorter, the energy in the particles can get bigger and bigger.
Over short periods of time they must “borrow” energy from the universe. And Einstein proved that energy and mass are equivalent. If the universe can borrow energy, why not mass?
The law of conservation of energy violated for short period – so also the Momentum ?
If the energy and momentum violated for a short period between Phases (fractal or foam), there will be great increase in Gravity ??
Isn’t it amazing how oft-repeated but misleading phrases, each one partially true, can be strung together to make nonsense?
“Einstein proved that energy and mass are equivalent. If the universe can borrow energy, why not mass?”
Read http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/more-on-mass/the-two-definitions-of-mass-and-why-i-use-only-one/ and then read http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/mass-and-energy/ .
And I haven’t even written the article about how wrong it is to say that objects “borrow energy from the universe”. The law of conservation of energy is NEVER violated, not even for a short period. Despite the fact that many physicists astonishingly make this statement, the equations we use are completely unambiguous in this issue. Time independence of a Hamiltonian implies energy conservation, without any uncertainty. Never in all of the work I have done over 25 years have I ever done a calculation in which energy (or momentum) was not conserved, even for a moment. However, mass (specially, what is sometimes called rest mass) is not conserved at all. The massive Higgs boson decays to two massless photons. No problem.
Thanks Professor, very clear teaching.
Mass means time dependent ?
Mass implies energy non conservation ?
Massive higgs decays to two massless photons – travelling opposite sides to two extreames of Universe – means, mass => momentum energy, then streaches into observable universe (space). ?
But why it is discrete. Is it both time dependent and time independent ?
For unambiguous conservation law and uncertanity, for massless photon, continuous Schroedinger evolution is somehow `nicer’, `preferred’, or `more fundamental’ than the “damned quantum jumps (discrete)” – Quantum mechanics without unitary evolution ?
….For unambiguous energy conservation and without any uncertanity… (the lower bound in the Heisenberg uncertainty relations for photons is the same as in nonrelativistic quantum mechanics).
Regarding uncertainty and energy conservation: let’s talk about momentum conservation because it is slightly easier to think about. Suppose I measure the position of a particle rather precisely. Then I have only a limited idea of what its momentum is. And now suppose this initial particle decays into two final particles. Clearly I have only a limited idea of what the final particles’ momenta would be, or what they would add up to. However, to calculate the uncertainty in what I know about the two final particles, the equations tell to me that whatever momentum the initial particle had was precisely distributed among the two final particles — precise momentum conservation. The uncertainties about the final particles is derived, without further uncertainty, from the uncertainty that resulted from my original position measurement.
To say this another way: if I had instead measured the momentum of the initial particle to high precision, then the total momentum of the final particles would be equally precise. The directions of the momenta would be uncertain, and set randomly — but momentum conservation does not determine the directions of the final momenta, only that their sum is the same as the initial momentum. So — what momentum conservation does not constrain is uncertain; but what momentum conservation does constrain is not any more uncertain than it was originally.
Energy is conserved but, mass (specially, what is sometimes called rest mass) is not conserved at all.
The measurement of the potential energy of the particle is akin to knowing its position. Kinetic Energy is a function of momentum, KE = KE(p).
The larger the apparent energy violation, the more fleeting the event. The uncertainty principle essentially allows the system to momentarily have enough energy for the particle to be in the forbidden region (tunnelling), with the proviso that it may not do so for very long.
So mass is more connected to momentum rather than energy.
Particle does not tunnel – can decay into massless particles (photon), within observable universe – but Mass decay to momentum, into stable vacuum.
Momentum is not conserved ?
Nothing is more connected to mass than energy, because mass IS energy. As the links Matt referred you to explain it is defined to be the energy in a specific (at rest) reference frame, but nonetheless mass IS simply the energy in the system in that frame.
Massive particles can decay into massless particles that nonetheless have energy and momentum. Momentum is always conserved in these decays.
The rest frame and reference frame is not equal basic law. But it appears equal due to momentum (inertia). Photon is massless only relatively.
Photons are absolutely massless. A single photon can not be made to have a mass in any reference frame under GR or SR. A *system* of a photon and something else (even two photons) can have mass, but not the photon itself.
Both photons and W, Z bosons were same – differ in “degree og freedom”. Masslessness is an axiom within “Dynamical symmetry breaking” – where Higgs mechanism works. But degree of freedom was made by Goldstone bosons in “spontaneous symmetry breaking”. It is a clear evidence, why “spontainity” in SSB is needed.
The didcreatness of Quanta shows a non zero blackbody and “mass and energy are not same” – it is only a Phenomenon under invariances ?
Degree of freedom at high energy makes radioactive decay. It will decay more at more high energy ?.
There is no difference between proton and neutron. The quarck gluon Dance (Dynamical symmetry breaking) is within Lorentz transformation (choreography within stage) – where higgs mechanism was originally intended.
But the Residual strong force is “out of stage, choreography”. Like “Double pendulum”, at lower energy, it is normal radioactive decay. At higher energy it is chaotic dance (nuclesr explosion). If there is Dynamical symmetry breaking, there is invariance – Energy = mass. But in SSB, it is like proton decay.
Why Higgs mechanism in radio activity ??
I don’t think you’d get many people to agree that protons and neutrons are the same, they have different electromagnetic charges and quark compositions and I don’t know of any symmetry that would join them. (And without the Higgs mechanism many of their properties are nearly unchanged.)
The Higgs mechanism doesn’t really operate as such in radioactivity. Alpha decays involve the strong and electromagnetic forces while beta involves the weak. Radioactive decay involving the weak force does not change much with temperature; there is a slight increase in beta decay rates but even at billions of degrees it’s not really significant. (Nuclear fusion increases at higher temperatures due to electromagnetic force being overcome.)
we have paradox, whether there is distinguish between proton and neutron or not, like in quantum decoherence, we “chose” one, ie.. the difference – that become 99% of the mass ?
I said increase in energy and decay in radioactivity in above context. At negative absolute temperature (below 0°K), we have paradox, whether it is hot or cold – we chose one. But in radioactivity there is CPT violation to choose another one also – it is decay ?
“Why my mirror image is not mine” ?
Because the Chiral symmetey is broken. We chose the massive real. In mathematical models we cannot choose massive part of the broken symmetey. If we go inside the mirror, like living below 0°K, we feel the real side as massless and mirror image as massive real ?
If the crystal formation have “almost non repeating pattern, it decays into other side of mirror image (vacuum) – without explicit breaking – the symmetry is just manifest itself in different way – if the Lorentz invariance is intact. But in radioactivity ?
“Time dilation was the direct result of the Lorentz transformation”.
Condensed materiald are never Lorentz-invariance, they always pick a preferred frame, the rest frame. But in Relativity, we have to choose.
So “spontainity” in SSB is important than, where it came from ?
When a continuous symmetry is spontaneously broken, massless bosons appear, corresponding to the remaining symmetry. This is called the Goldstone phenomenon and the bosons are called Goldstone bosons. This makes the choice.. ie.. the degree of freedom, where the speed of light as being ?
Rest frame is one reference frame, and the ability to choose whichever frame you want is a fundamental assumption of all Relativistic theories. Photons are called “massless” because in context “mass” implicitly means “intrinsic mass” or “rest mass” which is the energy a system has in the rest frame specifically — and in that frame a photon has zero energy. In any other frame, the photon has non-zero energy. If you want to use the “relativistic mass” definition of mass, then this means the photon’s mass is relative, excatly like its energy is relative, and precisely in the proportion c^2, because *mass and energy are the same thing*. Therefore to make the concept of “mass” meaningful, and something that doesn’t change with reference frame (like energy does), the “intrinsic mass” definition is used instead.
Anon, I agree 100% sir,
Mass = Energy, relative to the reference frame “chosen” – which was the choice of the nature – neither human (imperfect), nor the mathematics (try to copy human).
If we toss a coin it comes same head at some number, say at 5th – but not every time. Probablistically, we can predict that number – but only approximately. This “Quantization” leads to quantum correction – which destroys the “conservation”.
But observable Nature is without quantum correction + gravity + inertia = unnatural ?
“Nature chooses the smallest action – this is the Principle of Least Action (scientific Evolution – bu the fundemental is Involution ?).
If Nature has defined the mechanics problem of the thrown ball in so elegant a fashion, might She have defined other problems similarly. So it seems now. Indeed, at the present time it appears that we can describe all the fundamental forces in terms of a Lagrangian. The search for Nature’s One Equation, which rules all of the universe, has been largely a search for an adequate Lagrangian” – but the the Choice was “SPONTANEOUS” – it can go CHAOTIC, like in Double pendulum ?.
‘They laughed at Galileo, but they also laughed at Bozo the clown.’
Geocentrism is still alive, if not kicking, and it’s not all ironic jokes either.
Nature does not do science, nature just IS. It is we who do science, we who invented a system, a collection of ideas and ideals and gave them a name. Nature does not care how it itself works, nor wonder about such things. Only we (that we know of) do science.
Matt, welcome back!! While not a scientist, I really missed your regular blogs. The foundations you established in your early posts have prepared me to actually understand and even enjoy your later posts dealing with a lot of esoteric topics! I am looking forward to your discussion or dark matter and to your discussion over the next year or so on the news coming out of CERN.
Hi Matt, great article, looking forward to the next two.
I have a question about the distribution of energy in particle decay that relates to the conservation of momentum you have discussed here:
When an atomic nucleus (at rest) undergoes alpha decay (emitting a helium-4 nucleus and recoiling to conserve momentum), why does the emitted alpha particle have a well defined energy? (i.e. for a certain decay it will always be measured to be the same value).
Is it because there is only one possible way to distribute the energy of the decay among two particles (the daugther nuclei and the alpha particle) AND still conserve momentum, or is it because the daughter nucleus must have a very specific energy for some reason?
Compare this to, beta decay, where there are three particles produced and the energy of the emitted electron (beta-minus particle) can take a whole range of values – as there are many ways to distribute the energy between three particles and still conserve momentum? (I understand this was important in the discovery of neutrinos/the weak nuclear force).
“Is it because there is only one possible way to distribute the energy of the decay among two particles (the daugther nuclei and the alpha particle) AND still conserve momentum?” Yes! Precisely.
And your comparison to beta decay is apt; for decay to 3 or more particles, the energy of the outgoing particles is variable.
But surely beta decay proceeds through a w boson? Isn’t that a two particle interaction followed by one particle itself decaying into two more?
Interesting thought. I don’t know the answer but perhaps the nature of the W boson in the interaction (virtual particle) means that for that very brief period it appears to violate the law of conservation of momentum.
Matt, one of the many things I do not understand is this: what would give the dark matter transverse momentum? My thought is that the momentum would be generated by some sort of force, but if dark matter does not respond to electromagnetic, strong or weak forces, what would kick it? Neutrinos can account for transverse momentum because they are responsive to the weak force (if I am correct). In this I am thinking of Newton’s third law, maybe wrongly, but in that, wouldn’t the force that gives the dark matter its transverse momentum be expected to be equal and opposite to at least a part of the force that gave the particle you see its transverse momentum (with any additional also being equal and opposite to something else you see)?
No force is necessary for transverse motion to arise. Imagine a lone muon moving alongl, interacting with nothing. When it decays it will produce two particles (Electron and antineutrino). Since the rest masses of these particles are less than that of the muon more kinetic energy must be present. The two particles cannot move in line with the original muon; that would be an increase in momentum from nothing. At the least one particle would need to move ‘backwards’ so that the increased speeds ‘cancelled out’. But in such physics the two created particles can move apart in any direction. (To see why imagine the muon is sitting still.) So it’s almost definite that you will see transverse momentum arise ‘from nothing’ (And we do in fact see this in particle decays.)
At any rate the production of a dark matter particle will require some force to interact with both the creating particles and the DM particle. If no force could then no DM could be produced. (The weakness of gravity is why we can’t simply make graviton beams and study them.)
First, maybe I am wrong, but I see “created momentum” as ∫Force.dt. In the case of your muon decay, I am assuming at the instant of decay/creation the weak force imparts the momentum (equal and opposite) to the electron and the anti-neutrino, so consistent with conservation laws, the particles can fly off in any direction. However, my thought is that both electron and antineutrino feel the weak force, and it is not clear that dark matter does.
I agree with your second paragraph but the conclusion from that would seem to be that either the dark matter is created in pairs, there is yet another force present that we do not understand, or there is a lot more that I do not understand, the latter being certainly true.
It doesn’t matter what force dark matter feels so long as it feels *some* force. (and we assume it does, gravity.) In order to be created from the decay of a particle the daughter particles must be able to interact with each other and the parent particle. (The reaction must be reversible so an antineutrino and electron should be able to collide and form a muon.) If dark matter doesn’t feel any forces then it can’t interact with any particles and we can’t produce its particles.
So as long as we can produce any particle at all we should expect it, at least sometimes, to exit the collision with transverse momentum. This is of course not a common event, such ‘microcollisions’ may occur one in a million times so it’s not exactly easy.
I do not think there would be any dispute that dark matter feels gravity, but for such a particle to experience transverse momentum from the path of the event, wouldn’t that require a repulsive force, to push the particles apart? I confess to having dismissed gravity without much thought because (a) it is only attractive, and (b) it is so many orders of magnitude weaker than any others. The point of what I initially raised was, assuming the dark matter does not experience the weak force, and I also guess we don’t really know that, then we would not expect to find any dark matter in the LHC experiments. So, I guess the real question is, in the event we found some, would that imply that dark matter does experience the weak force, or would it indicate a further force of which we are unaware? And how do we tell? And if it were the weak force, what does that imply for the nature of dark matter? I just like to try to understand what a result will mean before I get it, which is why I am down this path.
You make some good points. It’s always nice to see a deep thinker.
No, a repulsive force is not necessary, the Higgs can decay into two photons and the Higgs force is always attractive. In the case of being created ‘via gravity’ we could imagine a high energy graviton decaying into two particles (Really unlikely which is why it probably would never happen.) or another particle spawning dark matter through a gravitational disturbance. (In the same way a proton makes en electron and neutrino via a W field disturbance.)
I think a big problem that I failed to address is that momentum isn’t created, *speed* is. The total momentum of a system is the SUM of all the momenta of the parts. from a physics point of view the transverse momentum doesn’t matter because it cancels itself out. It’s the same thing that lets you turn a gamma ray into an electron positron pair. (So you could think of one particle having ‘anti-momentum’ if you like.) This momentum arises because physics says you must balance energy and it’s exactly balanced because you have to conserve momentum as well.
If we see dark matter it’s a pretty good bet that it’s not due to gravitational interactions. The best guess would be the weak force (The electromagnetic would result in ‘not dark at all’ matter and the strong force is too strong to allow dark matter to be free particles.) or Higgs force but it could also be a totally unknown force or forces.
This is where the years or decades of further research come in. at first we wouldn’t be able to tell what was happening, only that *something* was. But the different possibilities make different predictions. If the weak force is responsible then the dark matter will be arising from particles that feel the weak force too. The first thing to do will be to determine how exactly (or not so exactly) the particles are being created as well as to pin down a few of its properties such as its mass. Once that is done we should have a good idea of the force involved. (A new force raises issue since it should have a force carrier that we haven’t seen from any other particle interactions yet.) After THAT even more research will be needed to see if what we have is dark matter or something else entirely.
Yes, the transverse momenta have to be equal and opposite to conserve momentum, no transverse momenta being there initially. That, to me, is due to the common force. Of course there swill be other ways to describe it, but they should say the same thing. I disagree with your example about the Higgs decaying to two photons (I am not disagreeing that it does, though!) as I see the two photons being electromagnetic phenomena, and while it may be stretching the use of the word “force”, I still see it as arising through electromagnetism, which is generated during the Higgs decay. (I do not know enough about the Higgs to state how – something that maybe Matt could post in the future?)
From my point of view, if the dark matter was subject to the weak force, that would, I assume, mean the standard model was incomplete, because as far as I know, dark matter is not part of it and it would mean that the weak force did more than the standard model predicts. If, on the other hand, it is not subject to the weak force, then it seems to me there has to be another force. Either of these would be good news in as much as it would give physicists scope to make more important discoveries. The worst outcome from my point of view is if the LHC now finds a desert in the extended range, but it is quite possible that it will.
I also appreciate the point that a new force should have a force carrier we have not yet seen, but if such a carrier only interacted with dark matter, then I doubt that we have carried out any experiments that would observe it.
You are correct, Higgs decay is a result of the Higgs and electromagnetic forces interacting. The *only* reason that the Higgs can decay that way is because it can interact with photons\electromagnetism. Particle emission is quite interesting; all particles have a ‘shadow’ in every single field that they interact with. So electrons for example have a ‘shadow’ in the weak field and the electromagnetic field and the muon field and… If it is unstable a particle can ‘dump’ energy from its field into any field it interacts with and make particles in that field. So the only way transverse momentum AND particle day can occur is via ‘feeling a force’. I hope this clears up y point.
Frankly any discovery would extend the standard model, the SM is pretty much complete now with the Higgs. The only question is what kind of addition there is, if any. This is why there are such conflicting feelings over the LHC not finding supersymmetric particles; it’s narrowing the alternatives and not providing any clue to what we’re missing.
One should perhaps note that the interaction of the Higgs with electromagnetism is indirect; it occurs through “virtual particles” (i.e. non-particle-like disturbances [fluctuations]) in the top quark field. That is, a Higgs particle interacts with the top quark field; so do photons, because top quarks are electrically charged. The top quark field, like any field, is always fluctuating; the fluctuations interact with both Higgs and photons, allowing the former to decay to the latter. See http://profmattstrassler.com/articles-and-posts/the-higgs-particle/the-standard-model-higgs/decays-of-the-standard-model-higgs/
Wouldn’t the particles that arrive at the detectors also collide with particles of the detector and possibly cause other side-effects that generate noise in the results? For example, what if that positron collides with an electron in the detector and annihilates? Presumably, other types of particles that collide with particles of the detector could result in other jets that are even messier. At some point, wouldn’t the detector itself become either gummed up with junk that needs cleaning out; or “ablated” from all the collisions that it is detecting?
All good questions. (a) The “side effects” you mention aren’t a bug, they’re a feature. We use the fact that the particles that arrive at the detector actually hit things, and leave electrical “noise”, to make the measurements! (b) The detector does not become gummed up — the number of particles in even a small chunk of detector is in the billions of trillions, so a few extra particles from LHC collisions don’t add much — but radiation damage from the effects of those particles does gradually degrade the detector, and this is why some parts of the detector have to be replaced after a few years.
Matt, I understand the limits of analogies, however, your diagram,
, is over simplified, considering you are at the theoretical limits searching for a hypothetical dark matter.
Where is the vortex motion in your diagrams?
All real objects create vorteces.
No they don’t.
If we hypothesize that dark matter exists, it would seem that there would be MANY high momentum transverse DM “particles” that are balanced by transverse DM particles in the opposite direction. Here, neither stream would be detectable so it seems that absolutely nothing constructive can be said. However (again assuming existence of DM), can anything be said, probabilistically, about how many streams of traverse DM would be expected to be theoretically “balanced” by KNOWN particles (such as the electron in your example)?
At an LHC collisions, you would likely only produce one or two dark matter particles at a time. It is possible you might produce a few more. But not streams.
Thanks, Matt, for your earlier reply to my question. Your final sentence said:
However, at some point this answer could devolve into a discussion about semantics. The only interesting thing, in the end, is explaining what we see, not precisely what we call it.
That was really the point of my question. Is there another interpretation of what we are seeing that does not involve dark matter as a particle? Could there be an alternative explanation that we just aren’t considering? e.g. as an as yet undiscovered property of space?
There could always be ‘something else’; it’s possible next week we’ll discover that black holes can be made in your kitchen. The more pertinent question would be what current alternate explanations exist, of which there are a few. Professor Strassler mentioned black holes and MOND. They’re possibilities, but not front runners.
There is evidence of dark matter every time a double slit experiment is performed; it’s what waves.
How mainstream physics is incapable of understanding de Broglie’s “subquantic medium” is the dark matter is beyond comprehension.
“… If we add up their transverse momentum and the sum is zero [or rather, if the sum is close to zero — because no measurement is perfect]..”
Sum should be exactly zero, why is negligence shown here? That negligible momentum might be the info, whcih we are looking for? And why is measurement never perfect?
No measurement is ever perfect. Period. Every experiment is made with a physical object that is not able to make perfect determinations of any quantity. That’s the first and most important thing that every experimental scientist learns. And that’s why 50%-90% of an experimental physicist’s time is spent determining exactly what the uncertainties of the measuremnt are, and why every new experimental result stated on this website comes with an accompanying statement about the uncertainties.
We are not mathematicians. We are not philosophers. We measure real things, and we obtain real knowledge. And no real knowledge is perfect. If you don’t believe me, I invite you to draw me a perfect triangle.
“Neutrinos, which LHC’s proton-proton collisions produce many times a second, go right through ATLAS and CMS without hitting anything, and leave no trace. Despite this, ATLAS and CMS can and do still infer that neutrinos have probably been produced, and they can use the same technique for dark matter.”
Speaking of questions that could devolve into a discussion about semantics, I have never seen a tangible, testable definition of “direct”. [And I may have said this before here.]
Quantum mechanics tells us we can never know anything ‘directly’ but have to observe properties. For example, when we see a tree we don’t see it ‘directly’, we observe its traits in reflected (or emitted) light. That is no different in principle from seeing its shadow projected on a wall, from the relative absence of reflected/emitted light. It is just more difficult to do and to get the same quality of observation – of being just as certain of seeing a tree and not an unfortunate juxtaposition of a pole and a bush, say.
Wandering into semantic land, I assume when people say “not direct/indirect” they mean ‘not as simple and low uncertainty hypothesis test (constrained observation) that I would like it to be’. Or is there a hypothesis test definition of this? (Which is the point when the suggested inference of ‘missing particles’ becomes a quantitatively asserted deduction of ‘n neutrinos’, with known uncertainty and all.) I ask, because I think the attempt of distinction may insert an unwarranted subjectivity.
I did beg the question!
The term “direct” has to be understood as context-dependent; I certainly don’t mean to be precise. We detect electrons and muons and hadrons and photons by observing their effect on the matter inside our detector; they strike atomic nuclei or strip electrons off atoms, and this leaves electric signals that our detectors are designed to pick up. That’s “direct” in this context. Neutrinos strike nothing and leave no electric signal in LHC detectors, so their presence can only be inferred from the apparent non-conservation of transverse momentum.. One impact of this is that we can’t tell whether one or two or three neutrinos have been produced and whether these particles are actually neutrinos or something else. By contrast, we can certainly tell the difference when one, two or three electrons are produced — because we have (in this sense) direct information about where they went and how much energy each one had.
Quantum mechanics? Philosophy has been telling us nothing is direct for centuries. How do you know your chair is real? you can see, touch and feel it? But that’s a measurement by the various cells in your body, filtered through nerves then the processes of your brain. Indeed how do any of us know we’re not brains in a jar? What can we really say we ‘directly’ experience?
We detect Neutrinos due to its connection with Radioactivity (weak nuclear force) – like goldstone bosons – accounting for missing energy.
The W and Z bosons reacts only with left handed particles. So to balance the conservation of momentum, there must exist right handed neutrinos ?
There is also conservation of so called spacetime or hypothetical flat universe ?
Dark matter does not belongs to this flat universe – unlike neutrinos ?
What is heavy ?
Neutrinos does not obey Unitarity principle – I think nor the Singularity.
Singularity says, at high energy, Rest mass forms Heavy elements, and thus the Black hole.
But there is “paradox”, what is negative temperature below 0°K.
So if there is Time dilation, there is no Rest mass – no singularity – no blackhole.
At high energy, instead of forming heavy elements, there will be Lighter elements and Proton decay – and Dark-energy star – MORE NEW SPACE, and time dilation.
The inertia of momentum (conservation) forms the rest mass. Stopping the “conservation of momentum” forms the energy into space.
Dark energy is negative pressure and anti-Gravity. Again due to the “paradox”, Gravity and momentum makes the Mass. ??
No, conservation of momentum has nothing to do with left or right handedness. What it means in the case of W\Z bosons is that you (should) never see momentum conserved simply between a right handed particle and W\Z boson.
Spacetime is certainly not conserved, the expansion of the universe puts paid to that idea.
Negative temperatures have been created; they are quite interesting since in a way they are hotter than any positive temperature.
Quantum critical phenomena: In such phenomena, small changes in the external conditions of a material can cause dramatic and anomalous subatomic changes, called quantum PHASE transitions, in the material’s properties.
The mass of compact astrophysical objects consists of the same dark energy (or SPACE) that makes up 60 percent of the mass of the universe.
This does go against the mainstream predictions of general relativists,” he said. “When I came up with this idea, people just thought I was crazy for many, many years. But in 10 years, this will be the orthodox belief. This explanation of dark energy stars will help explain dark matter. This could profoundly change our whole view of the universe.” -Champlin.
I have always found when someone says they will change the way we view the universe they fade into obscurity. When they say ‘I have no idea what this means’ we celebrate them in 50 years. Only time will tell. Frankly I think these ‘dark energy stars’ are just black holes by another name. (Especially if you factor in the recent ‘firewall’ fracas.)
Many thanks Mr. Kudzu, I fall in second Category.
If blackholes pull light (photons) also invisible (Dark) ?
If a vacuum cleaner pull something, it must be more faster than the pulled ?
Vacuum cleaners work differently than you would think. In fact the air is not being pulled into the cleaner, rather the air outside is pushing itself into the cleaner.
With black holes they do not ‘suck’ as we see so often in the movies. Instead one way of describing them says they curve space. Think of the Earth around the sun; the sun has curved the space. The Earth ‘thinks’ it is moving in a straight line but because of the curved space it goes around. If the Earth was sped up it could ‘climb the walls’ of the suns curving and escape. But if the curve is enough then nothing can go fast enough to climb out. Likewise we could view it in terms of energy and say nothing will ever have enough energy to get out. (The more you give it the more it needs.)
A big issue is that we do not ‘know’ how space works. The whole GR curving thing is our best idea but we know something is wrong somewhere because it is different than the QM gravitons and fields thing. Every time you hear ‘singularity’ in science it is code for ‘Nobody knows’.
Matt, what might dark matter be if not particles?r
There are many options in principle. It could be made of small but macroscopic lumps, of varying size, that are themselves made out of particles currently unknown. It could be made (though data is making this increasingly difficult) from primordial black holes. However, writing a theory (i.e. equations! with predictions!) in which these ideas work in detail, and are consistent with all known data, is not easy. That said, many things are hard until you see how to do them…
Is there any PHASE transition between “mono jet” and undetected (DARK) particles ?
Phase transitions are about large quantities of material undergoing complex interactions, not about three individual particles. So the question doesn’t make sense… not sure what you were thinking
Transition between quantum foams – one expanded, one was not during inflation.
In one, light travel at “c”, in another more than “c” because – in not expanded enormous space (if speed c is constant).
All our current theories state that no, there should be no such phase transition. Indeed if such a transition were possible we should have detected it by now, especially since it violates relativity.
Thank you Mr. Kudzu,
I read somwhere that due to imaginary momentum during tunnelling, there is possibility of more than “c”. So I imagined the dark matter is that momentum (rather than energy as mass). If the “space” is more, if the “c” is constant, it has to travel fast. Faster than “c” does not radiate electromagnetic waves (DARK) – it is not violating relativity ?
Moreover, rest mass is the mass at still. Potential energy is the energy at still. More mass is more momentum.
Potential energy tunnels. There is negative kinetic energy inside barrier, but energy is conserved.
But rest mass is not conserved – so also momentum is not conserved ?
Aaah. ‘Tunneling speeds’ are a different matter entirely! This relates to the ‘group velocity’ which can exceed c, but it’s a nasty trick. Imagine I race two mice down a track that move at the same speed and start at the same time. But, halfway through I shoot one mouse’s tail off. Now though both mouse’s noses pass the finish at the same time the ‘middle’ of the tailless mouse will pass first, going ‘faster than m’ because I changed the middle of the mouse by removing the tail. So it is when you send a signal through a tunnel; the wave packet changes ‘shape’ so that technically it exceeds c. More specifically you send a Gaussian pulse through some medium that gets saturated, so the later part of the pulse is attenuated, and then observe that the peak of the pulse arrives earlier.
As for ‘imaginary momentum’; this relates to the ‘poles’ of the momentum space wavefunction. The momentum space wave function only has physical meaning when the momentum is real, but the imaginary poles do have mathematical content. They tell you that the position space wavefunction has an exponential decay. This information is obtained from the theory of residues in complex analysis. The subject is complex and it’s easy to read it the wrong way and go ‘Speed of light is broken!’ in the same way some have announced that light has been ‘stopped’ in certain experiments. (The particles are not standing still, it is a complex effect.)
Potential energy applies to any energy that is not motion and the difference between potential and kinetic energy is kind of made up. If I throw an orange at you fast it still has lots of potential energy in its chemical bonds, atomic nuclei, the fact that it has not fallen to the floor yet… Likewise if I take a spinning blade whizzing around real fast and put it in a box the kinetic energy of the blade can become the potential energy of the box. (Hit the box and suddenly a blade cuts you in half. This is not as stupid as it sounds, a still hydrogen atom has kinetic energy if you count the moving electron and the moving quarks in the proton and…)
More mass is only more momentum is you have the same speed. Momentum is speed AND mass.
The barrier does not have negative kinetic energy, instead it requires energy to get over. This doesn’t have to be kinetic energy. A ball of gunpowder in a deep pit can escape if it catches fire and explodes out, using chemical potential energy to surmount the barrier. You can in fact say the *pit* has negative energy so that the particle needs to find some more energy to get ‘up to zero’ (Think of being in a hole, you obviously have less energy than someone standing on the flat ground.)
Rest mass is not conserved and speed is no conserved but momentum *is*. This is because mass and speed are just two forms of the same thing, energy. Say I have a fat, heavy particle like the Tau just sitting still. It decays to an electron and antineutrino, what happens? The mass has not been conserved because the two daughter particles are much MUCH lighter. But momentum demands to be conserved! So if the mass goes down the speed goes up, like a seesaw. The particles go whizzing away at nearly light speed. We see this all the time with radiation. The radiation does not wander about all slow and quiet, nosir! It rushes away and smashes into things.
Blackholes are invisible (Dark) because light (photons) could not escape.
Speed is time dependent. How much distance covered in what time. If massless photon have speed, it has momentum not altered without external factor.
Mass change to massless with speed “c” with conserved momentum.
If it enters a different phase with “more SPACE”, in order to keep the momentum conserved, it has to travel fast, to cover the same distance.
If two bubbles of same volume, one with more space, the light will travel faster in more space, in order to arrive at same time at other end.
Space itself is altered – neither speed nor the momentum.
No mass, no momentum. Momentum into more space.
So no electromagnetic radiation (dark) ?
Actually no, this is the interesting thing about light. To conserve momentum its speed does not change, but its *frequency* does. This can actually be easily observed. Think of shining a light straight up from the ground. As the light moves up it is fighting gravity, it should lose speed, but it can’t. So how does it conserve energy? The light gets ‘stretched out’; its frequency changes which means its momentum and energy drops. So light going to a place with ‘more space’ doesn’t move faster, but its frequency increases.
Thank you Mr. Kudzu,
Mass => photons => high frequency = less time interval (uncertanity) = high energy = High cosmological constant of the vacuum or dark energy.
So mass turns into dark energy ?
Protons Mass is momentum energy of gluons. At head on collision, momentum (mass) decays to SPACE.
Environmental effects accelerate proton decay. This may account for high-energy cosmic-ray sources and positron sources in the sky. When the matter falls through the event horizon, the energy equivalent of some or all of that matter is converted into dark energy or more space (expansion) ?.
I’m not quite sure I get your logic with ‘high frequency = less time interval’ I would note that a high frequency is NOT the same as lower uncertainty; I can *measure* the frequency of any photon and that will ave some uncertainty in it. In general the higher the frequency the more Hz my error. (So a 1% error in a radio photon of 100Hz is just 1Hz, but for a visible light photon it would be billions of Hz.)
When protons collide head on we have a pretty good idea what the energy becomes, energetic particles. What kind of environment would speed proton decay the trillions and trillions of times needed to make detectable positron sources? So far only being in an unstable atomic nucleus does that.
“Why my mirror image is not me” ? – Because the chiral symmetry is not broken, the quantization (discrete) remains the same. it indeed turns our right to left.
But the non-conservation happens in a tunneling process from one vacuum to another. Particles cannot tunnel, but waves can tunnel ?
But particle could tunnel between different vacua (phases).
The flipping (time interval) in electromagnetism creates magnetic dipole – like “discrete” quanta. I mean we cannot teleport matter within our universe, but possible between vacua. Mass is created because vacua reacts through Gravity – like dark matter, may be also through neutrinos. If mass could be created, it also decay to other vacuum. Even now considerable mainsteram says, Higgs field is a Tachyonic field (spontaneous symmetry breaking Goldstone bosons making it normal within light speed ?).
“If the distance between the atom and the mirror is very small, it is physically impossible to distinguish between these two paths”.
“The fascinating thing about this experiment”, the scientists say, “is the possibility of creating a quantum superposition state, using only a mirror, without any external fields.” In a very simple and natural way the distinction between the particle and its mirror image becomes blurred, without complicated operations carried out by the experimenter.
Particles *are* waves. Nonclassical waves but waves nonetheless. We have teleported matter in our universe, just not very big clumps of it.
That is an interesting experiment but not something I would call groundbreaking. I wouldn’t say it blurs the line between a particle and its mirror image either; the ‘mirror image’ is just that, an image, not an actual thing. What is being blurred there are two states, moving towards and moving away and you can do that with a particle far away from a mirror too. Indeed many ‘classic’ quantum phenomena involve mirrors. This just reaffirms the old adage, ‘If you can’t tell, you can’t tell.’
The actual change is not a change over time, but over space.
Particles *are* waves. Nonclassical waves.
I understand, if we zoom on particle, we find almost empty space – but fluctuvations (Time difference) ? – a kind of micro time dilation – making “flip” in electromagnetism, Quantum discrete in quantization. A Law as a fantacy – as nobody is perfect.
Waves turns to Rest mass, is also a Quantization – a Law as fantasy.
If the change is over space, not over time,
Quantization of “time difference” could only saved by perpectual Momentum ?
“Rest mass and Time dilation cannot coexist” – but momentum (Dark matter mechanism, like Higgs) can keep them exist.
GPS works because, Special relativity Time dilation slightly prevails over General relativity time dilation.
If, “change over space” prevails the both ?
In special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.) In contrast, gravitational time dilation (as treated in general relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree about the direction and the ratio of the difference. There is still some disagreement in a sense, because all the observers believe their own local clocks are correct, but the direction and ratio of gravitational time dilation is agreed by all observers, independent of their altitude.
The velocity time dilation (explained above) is making a bigger difference, and slowing down time. The (time-speeding up) effects of low-gravity would not cancel out these (time-slowing down) effects of velocity unless a space station orbit much farther from Earth.
The issue here is that in relativity gravity is identical to acceleration; if you are in a box and feel ‘gravity’ you cannot tell if that is real gravity or if the box is accelerating upwards. So just as acceleration ruins the reciprocity of time dilation so does gravity. Reciprocal gravity effects are possible, at least mathematically but they involve things like a changing gravity field that you don’t really get in nature. (That is something like the earth doubling in mass every five minutes, not ‘changing’ like gravity getting weaker.)
With particles ’empty space’ is kind of wrong. A photon has no ‘core’; nothing solid you could bounce a ball off, but the volume of space it is in is not empty, it contains the energy and fluctuating fields.(And the fluctuating fields are not from the particle’s perspective but ours! A photon does not experience time, it moves at c. Interactions with its oscillating fields is by other things, very curious.)
‘Rest mass’ is also kind of not true. It is the energy something has when not moving, but in all cases we know of this happens because the object is ‘moving’ in some way. (Particles in a proton, the flipping between particles in an electron.) If you ‘break things down’ all you find is energy.
In the case of gravity vs velocity they are in fact equal. At the horizon of a black hole where the escape velocity is c gravitational time dilation becomes infinite.(So if you observe something falling into a BH you see it redshift and slow down until it appears to stop on the horizon.) If velocity dilation dominated then time would ‘stop’ before a particle reached c.(Or, if you let time stop at c velocity you would be able to see inside event horizons, the gravitational effect on massless light would not be enough to redshift it to oblivion.)
“The issue here is that in relativity gravity is identical to acceleration; if you are in a box and feel ‘gravity’ you cannot tell if that is real gravity or if the box is accelerating upwards.”
Accelerated charges radiate. Charges at rest in a gravitational field do not. Does this violate the equivalence principle? Discuss.
Lorentz invariance makes this phenomenon. But it needs spacetime. Radiation itself a form of decay try to violate spacetime – but could not – W & Z bosons + Goldstone bosons could. Gravity is from global symmetry. I think it only weakly reacting – but we feel through mass and spacetime geometry ?
“If generally happens that when any particles of any type are produced’
A perhaps simple question: where does the transverse momentum come from in these collisions? Is it like the collision of two pool balls traveling in opposite directions which then move off in distinctly different directions or are there other processes at work (and here I am thinking of the composite nature of the proton)?
Perhaps put another way, are you looking at transverse momentum because it is (relatively) easier to detect with the instruments than particles travelling in the direction of the beam, or is there something special about the kinds of collisions/particles that have transverse momentum?
Lastly, you have remarkable patience.
Most proton-proton collisions are a sort of splat, something like two snowballs colliding.
But occasionally, within the overall collision there’s a very energetic “minicollision”, in which a quark or antiquark or gluon in one proton hits another quark etc. in the other proton with very high energy. This is indeed similar to (though definitely not *that* similar to) two billiard balls hitting really hard. As you said, in such a collision, the two balls will leave the collision moving in directions that may be very different from the direction in which they entered. This “scattering” of two billiard balls is similar to what happens with the scattering of the quarks/gluons, with the additional feature that instead of scattering, the quarks/gluons might do something more interesting — such as making a Higgs particle, which then decays to particles that go flying off at high energy but at random angles, often transverse to the beam.
So — you only see particles emerging with large transverse energy if there’s been a particularly energetic “minicollision” within the proton-proton collision. Most of the phenomena particle-physicists are interested in occur in energetic collisions that are non-splats, so that’s what we focus on. On top of that, collisions without such minicollisions are so common that there are simply too many to store, and even if we stored them we probably couldn’t find anything interesting and subtle in such an enormous vat of data.
Very interesting to see the real collision event and data you included and explained clearly for us, greatly enhanced the second section.
Eagerly awaiting the final part!
I cannot do better than Matt’s first sentence.
This comment was directed at Veeramohan’s comment to me below. I don’t know why it turned up here but I suspect I made a mistake in posting.
Here is a fact that questions the particulate nature of Dark Matter.When two stars or galaxies are in very close proximity they exchange matter. Dark Matter halos do not behave in a similar fashion under such circumstances.This suggests that the Dark Matter halo is not gaseous.
Curious, do you have a reference for that? I’ve never heard anything about that. What does the halo do? get left behind?
This is probably understood and taken into account for the missing mass (gravity) in galaxy’s, but couldn’t the central black holes themselves account for it? Could some black holes be more dense or more massive then predicted? Since there hard to detect and hard to theorize accurately.
One can measure the mass of the Milky Way’s central black hole quite accurately from stellar orbits.
Also, the dark-matter problem in galaxies requires the dark matter to be less centrally concentrated than stellar matter (and central black holes).
Thanks for reply Phillip much appreciated, so it is just certain systems of stars and galaxy’s that behave in dispute with GR while others behave as expected? …. That’s a powerfull argument then for a dark matter then as has been expressed. Thanks
As far as we have seen *all* galaxies behave anomalously in the same general way, but to varying extents. (That is they seem to have different amounts of dark matter in them.) There’s still a slim hope held out that this effect may be due to a strange property of gravity or some kind of ‘normal’ matter (Or smallish black holes or somesuch.) But dark matter is the leading theory so far.
Yes; the equivalence principle applies only locally. Radiation is inherently nonlocal, so the equivalence principle does not apply in that case.
Thanks kudzo, ahh I see now. So dark matter must be in different concentrations in different places. Do we see planets in other solar systems behave anomalous? (Technology permitting) Or just stars, galaxy’s and galaxy clusters? Could it be a matter of scale that alters GR somehow? Is that what these other gravity theories (MOND. ect) explore in a way?
So far we have no evidence of anomalous gravity on solar-system wide scales. There *was* ‘The Pioneer Anomaly’ but that turned out to be something normal. Even systems like binary stars and star clusters don’t show effects.
Initially it was thought that it might be the large scale that changes, say, the behavior of gravity. The problem with these theories was that they were too simple, it can’t just be a matter of gravity’s strength changing slower than expected. We see things like galaxies where the fastest stars aren’t in the middle but a little way out and galaxies that appear to be mostly dark matter while others have less. MOND isn’t entirely ruled out. (This modifies gravity and could thus be considered modified GR.) but it’s hard work making it match all the data. Right now we have more of an idea what dark matter isn’t rather than what it is. And thus we research.
Thanks kudzu, ……….. Umm yea, I see the issues now. Dark matter sure seems the strongest candidate. Yes research continues and you can’t beat a good mystery.
Thanks kudzu, …….. I see the issues now. Dark matter sure seems the strongest candidate. Yes research continues and you can’t beat a good mystery.
I think that LHC will search in the wrong high energy value for the Dark Matter, since it should be found on much lower energy range. The gravitational force attracting the matter, causing concentration of the matter in a small space and leaving much space with low matter concentration: dark matter and energy.
There is an asymmetry between the mass of the electric charges, for example proton and electron, can understood by the asymmetrical Planck Distribution Law. This temperature dependent energy distribution is asymmetric around the maximum intensity, where the annihilation of matter and antimatter is a high probability event. The asymmetric sides are creating different frequencies of electromagnetic radiations being in the same intensity level and compensating each other. One of these compensating ratios is the electron – proton mass ratio. The lower energy side has no compensating intensity level, it is the dark energy and the corresponding matter is the dark matter.
Only had time to read your article just now so did Not read all the comments. Excuse me if I am repeating any. First of all, you explained the detection of undetectable particle in an extraordinarily clear way. I feel I really understand what will be going on with the LHC experiments.
But, a second question: in the 80s (quite a long time ago) I was working along side a particle Physicist who was working on a method of automatic pattern recognition for collider pictures in order to do away with the immense amount of uninteresting data produced by colliders. Has work in this direction succeeded? Are non-transverse events recognized and jettisoned automatically? Thanks!
Yes, this is standard technique: see http://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/the-trigger-discarding-all-but-the-gold/
Is it right to say that even Higgs does produce dark matter in some decays, most dark matter in the Universe is produced in some different way?
We need some particle that decays mostly to dark matter and if this was Higgs it would be obvious by now that most decays have missed mass.
Matt, your most recent update talked about ways in which (perhaps!) dark matter could be created at the LHC via exotic decays of the Higgs or of another, new, non-dark-matter particle. It seems surprising to me that this could be a conceivable possibility, because it would indicate connections/conversions between regular matter and dark matter. I realise no one knows anything specific about dark matter and all we have are speculations–but nonetheless could you tell me whether it is your sense that most particle physicists would similarly be surprised, if we learnt that dark matter can be made from regular matter in this way instead of it forming an entirely separate regime of matter altogether? (Or am I thinking about it the wrong way?)
As I understand it, the emptier space the stronger the influence of Dark Matter. Is my understanding correct?
Could a discovery Electron Pairing above Superconductivity ,Nature, to direct to dark matter presence ?
Is possibility to say something to Higgs boson decay in two photons if mass of electron or proton is considered , what happens with Coulombic force – field ?
Dear Professor Strassler,
Thank you for the time, effort and energy you devoted to this post. You’re explanation is clear and very helpful to those among us who do not have a formal formation in Physics. Reading this article helped me understand the extent and limits of the experiments conducted with LHS. It is a definite mark of an experimented professor when he has the grace and humility to tell us what we know and, more importantly, what we do not yet know.
I would truly appreciate it, if you could, perhaps address the following question, while forgiving my naivete, but I do wonder why is it that Gravity is not bi-polar? Is it because, according to Einstein’s General Theory of Relativity, gravity is not a force, but a property of space-time and as such does not have polarity? I will stop here, lest I show myself even more ignorant in these matters than I should be.
Thank you, again for this site. It is very helpful. I am passing your site over to my son.
Dear professor Strassler :
We learned from your lessons here that there are no particles but a quanta of the fields ie. a specified localized bundle of the wave that we call a particle , and there are nothing solid or rigid , then what is meant by proton “” collision “” and hadron “” collidor “” as if it it a collision among rigid bodies ? In addition since the quanta bundle is a wave then why the opposite moving protons does not just go thru each other without any sort of a real collision as it is normal wave behavior to go thru each other ?
Professor Strassler :
Is it possible that what we are looking for in the S.M. actually exists beyond S.M. in a totally still unknow theory so we will not be able to know what to search for for time being ?