1934: This is predicted
1997: This is done http://www.nytimes.com/1997/09/16/science/scientists-use-light-to-create-particles.html
2014: We will "demonstrate the feat within the next 12 months"
2015: Didn't bother
"Photon–photon scattering and other effects of nonlinear optics in vacuum is an active area of experimental research, with current or planned technology beginning to approach the Schwinger limit.[5] It has already been observed through inelastic channels in SLAC Experiment 144.[6][7] However, the direct effects in elastic scattering have not been observed. As of 2012, the best constraint on the elastic photon–photon scattering cross section belongs to PVLAS, which reports an upper limit far above the level predicted by the Standard Model.[8] Proposals have been made to measure elastic light-by-light scattering using the strong electromagnetic fields of the hadrons collided at the LHC.[9] Observation of a cross section larger than that predicted by the Standard Model could signify new physics such as axions, the search of which is the primary goal of PVLAS and several similar experiments. Even the planned, funded ELI–Ultra High Field Facility, which will study light at the intensity frontier, is likely to remain well below the Schwinger limit[10] although it may still be possible to observe some nonlinear optical effects.[11] Such an experiment, in which ultra-intense light causes pair production, has been described in the popular media as creating a "hernia" in spacetime.[12]"
Has anyone ever wondered why the C^2 in E=MC^2 I'm sure it wasn't chosen at random just because a large constant was needed, it must fall out of some other physics equations.
But still, what does that mean? What does the transmutation of energy into mass or visa versa have to do with the universal speed limit?
I am always struck by the inexplicable power of mathematics to describe the physical laws of the universe, in often simple equations like this. It doesn't have to be that way as far as we know.
Mass is a state of energy. c^2 turns out to be the conversion factor when you're turning things from our units of mass to our units of energy.
From the cosmic perspective, 'mass' is energy in a state that, instead of traveling at the speed of light, wants to sit on one place (for reasons that were discovered later), and needs a push to get it moving. When you measure mass, you're really measuring how much you need to push a given amount of this inertially-fixed energy to impart a given velocity. Our ordinary units of energy, mass, and velocity came from observing these facts of physics before we figured out what mass and energy "are", and E=mc^2 ties the knot between the different units we came up with.
The really fascinating thing is that Einstein was able to propose E=mc^2 before any of that was known. It was just a funny term that showed up in the equations for relativistic energy and momentum, and somehow Einstein's intuition was that it might mean something more.
I read a lot about physics trying to understand this stuff on pop-science level at least, but your comment really gave me a new perspective about it. Thanks.
Can you recommend an idiot-friendly source to read about this mass-energy relationship in more detail?
It is one of the assumptions of Einstein, namely that there is a fixed max velocity c. To get Newton's 1/2mv^2 in the Taylor expansion requires a factor c^2.
Something else would lead to measurable deviations in slowly moving objects.
E = mc^2 is the energy contained within a particle of mass m, IF it is at rest (has zero velocity with respect to your frame). If it is moving, it's energy is given by E = ymc^2, where y (gamma) is 1/sqrt(1 - v^2/c^2). This may sound like the particle has somehow "gained" or "lost" energy just by switching frames, but so has everything else. The differences in energy have been kept the same, which is all that really matters.
When deriving this formula for the energy it becomes clear that _any_ multiple of ymc^2 is conserved. We choose E = ymc^2 and not, say, E = 5ymc^2 because in the Newtonian limit (as speeds approach zero), the ymc^2 formula reduces to the well-known E = 1/2 mv^2, which is the kinetic energy of an object obtained from classical mechanics.
I'd really recommend reading a mathematical treatment of special relativity, because you'll be exactly clear on where this formula comes from.
I think the answer we want now is a non-mathematical one. It gets tiresome how most of the "answers" are just too afraid( or maybe naive?) to just say "we don't know" why the speed of light is the constant of proportionality in the mass-energy conversion equation.
You can answer the "how" very well which is what the mathematical derivation is, and which is what most people are answering in this thread but you see that none of those answers start with "Because..." but rather just keep on spitting out more math. And what we want is an explanation for why c^2 is there and what it means.
We don't know what it means, we haven't answered that question and we don't know how to answer it. It's similar to how pi keeps coming up in a lot of equations and we struggle to understand why.
> I think the answer we want now is a non-mathematical one.
I'm just an interested lay person, but my understanding is the past century of physics is a giant argument for trusting the math, and accepting it as explanation.
If someone asks "Why does xyz act this way?" then the best answer for it, once you get to non-intuitive quantum scales is: "because the math says so." Dirac's prediction of the existence of antimatter, the Higgs, and pretty much all quantum mechanical behavior are great examples of this.
Nima Arkani-Hamed, a kickass theoretical physicist, has a great lecture series on the philosophy of physics:
In an aside, he mentions that he used to explain the Higgs field with analogies such like calling it a kind of "molasses" slowing down particles and giving them mass. He's stopped doing that, because the physical analogy is really misleading. The true reason the Higgs as we conceive of it exists is that it addresses mathematical issues in our treatment of bosons that have mass.
The math said there was an issue. 50 years ago the math said the Higgs fixed it. It took 50 years and construction of the LHC, but now we've verified the existence of the Higgs.
The c² is not central, you can work in a set of units such that the equation is E²=m²+p². If you decide to add a unit for mass, then you naturally need a conversion factor with units of speed.
This is the first part of the Explanation. It is indeed E²=m²+p², but the p is the _relativistic_ impulse. For practical proposes you usually want the classical impulse p_0 in this equitation. And is a way easier to see how c shows up in the conversion between these two.
It's the proportionality constant between rest mass and energy. Mass times speed squared has units of energy. Same thing for the pc term: momentum times speed is energy.
To explain how we figured out the constant is c is a bit more complicated. The wiki article Introduction to Special Relativity is a good way to start if you want to understand everything well.
more completely, it's E^2 = (m c^2)^2 + (p c)^2 where m is the rest mass of the particle and p is the current momentum. It's a nice triangle relationship.
As for the interpretation thereof, you're going to need someone else.
No one has answered your question. There is no answer really to your question. At least, not to the level that you are asking. Why is c^2 in that equation? What does it mean? We don't know. It's a deeper level of understanding that we haven't achieved.
Another similar question would be why does pi come up in everything? There's a lot of physics where pi comes up and we don't know why.
The original question has perfectly satisfying explanations accessible to anyone who knows algebra and is willing to spend a few weeks studying special relativity. cynicalkane above provides a great intuitive summary.
Likewise, generally speaking, when pi comes up in physics equations it is a geometric factor, either having something to do with the bona fide geometry of the system (e.g. the capacitance of a sphere) or with normalizing some relevant probability distributions. Name one example where we struggle to understand where pi comes from in physics formula!
I strongly disagree. We don't know the answer to everything, but we have solved this question - in terms of other, more fundamental things that we haven't fully explained yet. It would be disingenuous to pretend that because we have solved the deeper layer, we can't give an answer at the shallower one.
Summary: Matter creation is the conversion of massless particles into one or more massive particles. Since all known massless particles are bosons and the most familiar massive particles are fermions, usually what is considered is the process which converts two bosons (e.g. photons) into two fermions (e.g., an electron–positron pair). This process is known as pair production.
In theory if you crank up the energy high enough, you'll create a bunch of Higgs bosons as well, though of course as always, they'll immediately decay.
the results must have the same total spin (0) (this might require that all the resulting things have spin 0 but I don't know)
the results must conserve a variety of other quantities,
I think maybe pairs photons are (one of?) the only things that meets these requirements?
I'm not sure. I'm mainly guessing.
But, if proton collisions can cause Higgs Bosons, I think maybe the idea is that so long as all the quantities are conserved(charge, mass, color, spin, momentum, etc. etc.), any particles with small enough energy can be the result maybe?
I don't know if that is the idea. I'm just guessing based on how things are described wrt protons, but I might be misinterpreting things.
I imagine "matter" as commonly understood would contain at least electrons and protons, but they would just be making electrons and positrons. Can we make protons/neutrons out of light too?
Yes, in theory quarks and their anti-particles will be created just the same as electrons/positrons. However, a) it is a lot easier to detect electrons/positrons than it is to detect quarks and b) protons are significantly heavier, so you'd need quite a bit more energy. Really the best way to think about this is just a particle collider, but colliding photons instead of matter. You'll still get a whole sea of debris that you can sort through and find interesting physics, but just detecting electrons would be a good first step.
With a lifetime on the order of a microsecond at best, it would be an interesting challenge to build anything out of it. Assuming I understood Wikipedia correctly.
In the beginning, there was nothing. But it was a very active kind of nothing that, because of the Uncertainty Principle, allowed bits of energy to be borrowed from nothing, leaving behind holes as a sort of IOU.
The likelihood of a virtual particle pair arising was inversely proportional to the energy difference across the pair. Since you need a fair bit of energy to do anything interesting, nothing happened for a very long time.
However, since there was an abundance of very long time, eventually two of the photons borrowed out of the vacuum with sufficient energy interacted in such a way as to give rise to matter.
Multiply that very long time by all of the matter in the universe (a very long time, squared; lucky we had lots of it) and we have beaches and sunsets.
The only remaining question is how all that matter was gathered into the singularity that gave rise to our present universe about 13.8 (or whatever) By ago. Maybe it accreted out of the original matter over another very long time.
Or maybe the idea that when you run the expansion of the universe backward you get a singularity is wrong. Maybe matter arising out of the vacuum disappears back where it came from when you run the picture backwards and it only looks like the universe started 13.8 By ago because that's how far out the event horizon sits. Maybe the cosmic background is the signature of the vacuum-derived pairs creating matter. Maybe this experiment will demonstrate an alternative origin for the cosmic background.
If this can be made practical at any scale, I think the most exciting applications will be in long-range space drives. Although it sounds as though immense amounts of energy are needed, not needing to take along matter to eject in order to move is a game changer for space exploration.
No, for the same reason that burning fuel in a cylinder to turn a crankshaft is more efficient than using fuel to make fertilizer to grow feed to feed horses to pull your cart.
