Ep. 287 E=mc^2

It’s mind bending to think about this, but the light in your house, and the house itself are really the same thing. Matter and energy are interchangeable. This was the amazing revelation made by Albert Einstein, with his famous formula: E=mc^2. This is the process that the Sun uses to turn hydrogen into radiation through fusion, and the terrible damage from a nuclear weapon.

Show Notes

Transcript: E=MC^2

Fraser: Astronomy cast episode 287 for Monday, December 31st, 2012, E=MC^2
Fraser: Welcome to Astronomy Cast our weekly fact based journey through the cosmos. We hope you understand not only what we know, but how we know what we know. My name is Fraser Cane, I’m the publisher of Universe Today, and with me is Dr. Pamela Gay a professor at Southern Illinois University Edwardsville. Hey Pamela how are you doing?
Pamela: I’m doing well how are you doing Fraser?
Fraser: Good, and we’re back from our awesome cruise in the Caribbean with 90 of our astronomy cast friends… and that was super fun.
Pamela: Yes, and we are going to be repeating this. Look for news aboutHawaiiin January 2014. I’m working on putting together a website on that. All the photos from this year will go up and information for next year will follow.
Fraser: Yeah, it was a really wonderful experience. Big thanks to the folks who did the end of the world cruise for inviting us onboard and letting us participate, we had a great time. Both with being able to see the ruins and do the excursions, but also, just to be able to spend time with the astronomy cast fans. It was great. You put together a really busy schedule where we were recording shows almost every night or doing events, meet and greet party, doing shows, stargazing every night out on the back of boat, we did lunches and dinners with the fans. We had the chance to hang out with almost everybody that came and so it was great to get to know everybody and of course to hang out with you, and the families got together. It was really a fantastic time and I can’t wait to do it again.
Pamela: I have to send out props to Victoria, Eric and Phoenix for all the help the day we went to Copa because you abandoned us and they helped us bring up the front.
Fraser: (Laughs) Yeah, yeah. Abandoned you… I didn’t want to send my children in to that nightmare gale force storm. But anyway,
Pamela: You made the right choice. We had the ferry ride of evil that you can read about in the future in my blog.
Fraser: Yeah we got some great pictures and so like you said it was a great chance to experiment and it was great to hang out with everybody but the downside was it wasn’t the best platform for doing astronomy related stuff because the boat moves at night and then it stops during the day. You’re carrying around horrible light pollution. The boat is moving so you can’t set up telescopes. So it wasn’t a great place for the kind science that we want to do so that’s why we’re going to look for a place that’s on land that’s near a nice observatory and we’ll figure that out. More news coming, just wanted to give everyone a wrap up, it was a fantastic time. Cool, Lets get rolling then.
Fraser: So, its mind bending to think about think about this but the light in your house and the house itself are really the same thing. Matter and energy are interchangeable. This was the amazing revelation made by Albert Einstein with his famous formula E= MC ^2. This is the process that the sun uses to turn hydrogen into radiation through fusion, and the terrible danger from nuclear weapons. So I think I can remember that being when I finally wrapped my head around this, and we did it in physics class in grade 11? Grade 10?, When we were given that formula and now we understood what that formula was about and we had to calculate, here’s your energy, how much mass, how much energy can you release, that they’re interchangeable. That was for me, it really felt like I looked at the whole world in a different way, because you’re so used to these things being two different things and now they’re not. So first let’s talk about this equation. What is it saying? What is it talking about?
Pamela: Well at the most fundamental level it’s saying that if you take something, it has a certain amount of material that makes it up and that material can get transformed into energy. But the thing as a whole has a sum of energy and mass that is a constant so you have the energy of a constant that is tied up in its rest mass and it’s kinetic motion and then you have the fact that if its moving, its matter amount doesn’t change. Its matter is dictated by how many electrons how and many protons does it have, but its momentum, it’s ability to act like mass, changes. This is a really confusing concept, but the best way to think about it is if you have two observers. Both looking at the same event they need to see the same thing and since time changes based on how fast you’re moving; if I’m watching a train moving at close to the speed of light, it would be very hard for me to watch it, but ignoring that, I would see time for the people on the train slowly approach a stop. This means that if someone were to drop a really nice pot, it would appear to very slowly drift towards the bottom of that very quickly moving train. Now a very slow moving pot should just gently touch the ground, but the reality of it is, is that if it weighs enough when it touches the ground there will be no gentle about it, and it will shatter into a million pieces. It’s equivalent mass, its relativistic mass, it has to increase in order for it to shatter when it hits the ground, in this, I perceive time moving very slowly for the people on this fast moving train. Now at the same time, for the people on the train, it’s a normal pot, you dropped it, this sucker moves fast, the thing shatters into a million pieces. It’s because of this change in relativistic mass that we are both able to perceive the exact same shattering of the pot.
Fraser: So then let’s actually look at the formula itself, break it down bit by bit. Lets start with E, what’s E?
Pamela: Energy
Fraser: Energy, as measured…
Pamela: It’s the ability of something to do work if you rest enough of the bits out of it.
Fraser: So typically it’s measured in Joules? Megajoules?
Pamela: Calories
Fraser: Calories, okay that’s E then M?
Pamela: Mass
Fraser: Ok so that’s mass in kilograms, grams?
Pamela: yeah
Fraser: Ok, C?
Pamela: Speed of light, kilometers per second or meters per second depending on what you decide to use. The normal units are meters per second, mass in kilograms and energy in joules.
Fraser: and then you square the speed of light and that’s where it gets ridiculous, right? The speed of light is already 300,000 meters per second and then you square that number and you get whatever you…
Pamela: Well it’s 300 million meters per second, 300,000 kilometers per second. So you take 300 million meters per second, and square that sucker and, yeah that’s a large number. What’s neat about this is if you turn this equation around and look at it as a ratio instead, the energy tied up in an object divided by its mass is always equal to the speed of light squared and that’s just kind of cool.
Fraser: When you think about, as an example I have here a nice little iron meteorite.
Pamela: Hey I’ve got one of those too!
Fraser: I know, (Laughs) we all do, we all do. It’s a phil-plate meteorite, if he really likes you he’ll give you an iron meteorite. And so it’s like 40 grams or so but there is enough energy to power a city in this piece of metal.
Pamela: For a brief period of time, yes.
Fraser: Yeah it’s a phenomenal amount of energy locked up in all the matter around us, in fact its as if everything around us are bombs waiting to go off. ,
Pamela: Frozen energy?
Fraser: Frozen bombs but the trick is unlocking that energy, that’s the hard part. So lets get back to Einstein then. You already lead into it which is the Relativity concept, so how did Einstein come up with this idea?
Pamela: What’s interesting is that initially there was no E=MC^2 in his paper, it was kind of this sentence off to the side that, according to the translation of the German that I stole ruthlessly from Wikipedia, it said that if a body gives off the energy L in the form of radiation its mass diminishes by L/V^2. This has to do with how the momentum is effected in the process it has to do with the conservation of kinetic energy tying into everything. It was only later that Max Plank was the one who wrote that the mass that is initially in a system is equal to the energy initially in a system divided by C^2. It’s very important that you think of this in terms of mass and not matter because mass and matter are not really interchangeable. Matter is frozen energy, but when you have something, potato for instance; potato is everyone’s favorite example. That potato is made up of a certain amount of particles, and those particles are matter, they are tied to the Higgs boson, they have a mass because of that, but the amount of matter in it is a specific thing. The amount of mass is different and it’s hard to sort that out because you can pull apart an atom and depending on what it was when you started you still have the same bits, but the energy of the bits has changed and the mass energy is conserved and the matter is something different and you can actually, if you take a bunch of energy, you can turn it into matter but the mass energy is conserved.
Fraser: How did this even occur to him?
Pamela: He’s a genius?
Fraser: Well I understand that but you were saying this before that he was thinking about the implications of mass moving at relativistic speeds, that it being equivalent to energy had to be the outcome, right?
Pamela: It falls out of the equations naturally, that’s one of the disturbing things when you’re asked to do all these homework problems in general relativity and special relativity. This is one of those things that when you start looking at “how does momentum change as an object accelerates” and you take into account relativistic corrections. When you start looking at all these different things it just falls out naturally that you have this E/M=C^2 and that’s how it falls out naturally. It doesn’t fall out at E=MC^2 it falls out as the speed of light squared just happens to boil down to energy divided by mass.
Fraser: So back when Einstein first proposed this equation, you mentioned that the next plank had refined it, did Einstein come back around and give it its final form?
Pamela: Einstein did return to the topic. He did write E=MC^2 and was the title of one of his articles, but by the time he got around to doing it, it was already generally being used. That’s one of the great things about science, is, while it may take us a while to decide how we’re going to generally refer to things and what we’re going to name things; once that relationship is discovered, everyone uses it. In this case he wrote down a brief sentence and it got out and got written out, everyone started using it and he did get credit because he was the first to write it down but him writing E=MC^2 did take a little longer to get to.
Fraser: I guess, again, back when he first devised this, this was the beginning of the 20th century, right?
Pamela: 1920’s and then he continued working on it through the two World Wars.
Fraser: Right, okay. They didn’t have a lot of practical applications or ways to even test this out that much?
Pamela: Well, in Astronomy we are starting to figure it out. What’s kind of amazing is that they did have to use all these sorts of things when they were starting to figure out the quantum mechanics of what drifts stars and when they were looking to figure out nucleosynthesis in stars. There are a lot of ideas that this influences. You need to have this energy idea that’s linking between mass and energy to start to consider nucleosynthesis, nuclear reactions, and nuclear bombs. It’s the foundations for a lot of very scary and powerful, and I mean that literally, powerful ideas.
Fraser: Right, so I guess you have the situation where the astronomers are like “We don’t know how stars work, we think they burn.” You can’t get that much energy…
Pamela: (Laughs) Well Evington had figured it out but we were still working on the details. Evington did some good work for us in the turn of the century, they’re all compatriots of each other.
Fraser: Right, but you’ve got a situation where you finally have a mechanism, you can finally understand what that mechanism is and what that relationship is. But I think where a lot of people really think about E=MC^2, they think about the nuclear program for WWII.
Pamela: Right and this is where, when you think of TNT, plastic explosives, when you think of most conventional weapons, you’re looking at a chemical reaction that when it takes place gives off huge amounts of energy compared to, like, mixing hair dye, which releases a small amount of energy, this is why they say tear the cap off of the hair dye before you mix it. Sorry if that was a little esoteric for all you men out there.
Fraser: You dye a lot of hair Pamela so we know why that’s on your mind
Pamela: I do dye a lot of hair, yes. So lots of chemical reactions give off energy. A lot of them also will take energy from their environment in the containered reactions going in will feel cold, but if a reaction is exothermic enough, energetic enough, it will release energy that actually shatters the chemical reaction going on. It releases so much kinetic energy into this system that things blast apart. But this is a chemical reaction, it has to do with the binding energies of the chemicals involved and that binding energy getting transformed into kinetic energy and thermal energy. With nuclear reactions you’re just taking the atoms apart and taking the energy of the atoms and releasing that and that’s a lot more powerful that just a standard chemical bond of whatever sort you’re dealing with. So now you’ve gone from the potato powering the, chemical means, a light for a science fair project, to all the energy in the potato poweringNew York City.
Fraser: So you really are getting that conversion of the mass into the energy of the potato.
Pamela: …the matter into the energy
Fraser: Yeah the matter into the energy where you actually blow up that potato at a nuclear level.
Pamela: Right and luckily, potatoes do actually resist this. But the other side of this, everyone thinks about the death and destruction and mayhem that you can do with nuclear weapons, and they look at the evil side of the equation. What’s kind of awesome is the converting energy into matter side of the equation. You and I are just frozen energy. We don’t think of it that way. But when our universe formed, our entire universe was nothing but energy and it took the universe expanding and cooling for that energy to finally be able to freeze out into matter, into protons, into electrons and neutrons came in eventually. There was early nuclear reactions and all of that was, a transformation process of nuclear energy into matter. Today in our quest to try to understand the particle physics world, we’re taking particles, electrons and protons, colliding them at high velocities inside of various types of accelerators depending on what we’re looking for and it’s in the energy of that collision that we look for particles that come out of that energy, the kinetic energy that’s transformed into something we may not have realized existed before.
Fraser: So what is the process? We talk about turning energy into matter and matter into energy, what is the process to, say, turn energy into matter, for an example? How can science do it now?
Pamela: Well it’s a matter of overcoming the forces in the center of the nuclei. Normally you have protons and neutrons in the center of the atom that are held together with “glue-ons”, because we are boring in naming the things that hold our atoms together, but at the same time they are repelling each other. This is the strange dichotomy, that causes atoms to get more and more unstable as they get larger and larger. Eventually when an atom gets too large it gets unstable and splits into something more stable. Now if you’re able to take and squish those particles together even more, you eventually overcome their ability to be stable and separate from one another, and in that moment of being crushed, they’re forced to become energy so you’re overcoming the nuclear forces inside the atom.
Fraser: Right, and how practically do they do this, say, in a nuclear reactor?
Pamela: Well in a nuclear reactor they don’t bother with the full atom. They strip it out to it’s simplest pieces, so you take two protons and collide them with so much force that in the moment they come together, the ability of the protons to repel one another, is overcome by the fact that they’re already flying together. That force of repelling doesn’t have time to slow the interaction enough and as they come together they end up converting into pure energy as they smash and they can no longer exist as protons.
Fraser: Okay. Its, again, almost the most efficient way to do this, the most efficient way is matter antimatter, but you had to have already built your antimatter in the first place right? Which is complicated.
Pamela: I’m not sure that there is any more or less efficiency in it, they’re just different. In both cases you’re releasing energy and it’s eventually freezing out as particles, but yeah, creating antimatter is a bear, and yeah, they’re just different.
Fraser: Okay so lets go the other way, lets go from matter into energy
Pamela: Well this is one of those neat parts that if you have a pile of energy hanging around it will naturally collapse into a particle and anti particle that have conserved momentum and fly off in opposite directions. This is something that’s going on all the time. There’s reactions ongoing on a regular basis where we have for instance beta decay and anti beta decay processes where neutrons break down into electron and anti electron neutrino conserving the momentum, conserving the charge, all the little bits. There’s all these conservationals that we have to pay attention to and one of the things people don’t seem to acknowledge is that there is anti particles everywhere, they’re generally anti neutrinos but they’re everywhere and a little bit of antimatter is not going to hurt you
Fraser: A little bit of antima… (laughs) Right? They use it for medicine right? They drop a little bit of antimatter in your body and watch as it explodes inside of you.
Pamela: (Laughs) No, they usually take a bit of normal radioactive matter that as it undergoes radioactive decays it does release beta particles and…
Fraser: I thought there was a form of it where they have, what was it? Positronic emission technology? Anyway, but the point of it is that scientists are using antimatter in their daily work these days.
Pamela: And we’re not blowing up the planet, it’s really not a concern. Antimatter exists, we’re not really sure why regular matter is the dominant one in the universe folks, we’re still working on it. The fact of the matter is that antimatter is everywhere, it’s just the minority form of matter, don’t hate on the antimatter.
Fraser: So there are free floating anti particles floating every now and then, and detonating?
Pamela: I think detonating is probably too strong a word.
Fraser: Annihilating, that’s the word isn’t it?
Pamela: So in general the anti neutrinos that are passing through your body they don’t want to interact with anything. They don’t want to do you any harm. They are the most antisocial of particles and so the probabilities that anything bad is going to happen; the probability that we could detect these suckers when we try is very low so we don’t need to be worried. And yeah, positrons happen too, they can do damage, this is why one should avoid radiation… but what’s a few neucleotides in one??
Fraser: What were the, sort of, moral implications of this equation? I know it caused Einstein a lot of, I don’t know, I think he was quite sad when he realized the implications of this technology, or of this equation and what it could be used for in terms of great destruction.
Pamela: That’s the thing: Science can be used for good and it can be used for evil and morality doesn’t often keep up with technology. There is always the question of dominance and humans like to be dominant over one another and here he was working to understand all the science that would lead to all of the positives: GPS. We have GPS because of relativity; understanding the formation of our universe is grounded in understanding relativity. But the other side of that was realizing exactly how fusion and fission can occur; realizing how to form hydrogen bombs and how to form nuclear weapons from plutonium and uranium, depending on your methods. It was this realization that we can cause runaway nuclear reactions if we trigger them correctly. That was the foundation of the Manhattan project during WWII and if it had only been used as a “Look at how big of a stick we have, now everyone be quiet and stop fighting” that would have been better, but the reality is, we dropped two bombs on Japan. I’m not going to argue the morality of that. I wasn’t alive, I haven’t studied it in detail. The reality is that we now live in a society that there is an ease of obtaining nuclear materials and it’s possible to conceive of the crazy intelligent suicide terrorist that creates the weapon in a suitcase. Luckily the technologies are hard to get a hold of, they’re extremely expensive to get a hold of but as miniaturization takes place, as technology drops in price we have to be concerned of the future where the suicide bomber isn’t carrying TNT or plastic explosives but the suicide bomber is carrying a dirty weapon and that’s a terrifying future and we can only hope to try and avoid it.
Fraser: Yeah, you can only imagine what they were wrestling with when they started to realize the implications of the math, of the physics, they were uncovering. Then on the one hand it was clearly possible to use this for great, you know, power plants and reactors and you can power ships and cities with this. They didn’t understand the waste issue with all this kind of stuff, but they could see it used for great good. Then on the other hand you can detonate these things and you are using them for great evil. How do you begin to communicate this to the politicians, because at the end of the day it’s just nature right? Reality says this all works…
Pamela: And it’s this horrible trade off. I’m a strong advocate of safe nuclear energy, the problem though is what is right and what is safe and what is good is often destroyed in the face of what is cheap and how do we make the most money. And because humans aren’t perfect there’s always going to be that person who looks at the trade off of probabilities. The “if we don’t spend this $100,000 there is a fractional increase in potential hazard”. And those sorts of decisions, the decisions not to spend the money for reprocessing, all of these decisions add up to a society that’s not ready to be fully responsible for nuclear energy. We live in a geologically unstable world and that requires even further expenditures and further risk and this is something thatJapanis struggling with greatly right now. It’s a small nation, it’s one of the most environmentally conscience nations in the world. They even tell you how to correctly recycle lipstick.
Fraser: Yeah, a special box just for the lipstick.
Pamela: It’s really something to be profoundly proud of. But at the same time they are such a small nation, they need nuclear energy. They’re a geologically unstable nation and they’re a technologically driven high energy demand nation and now they’re trying to struggle with “how do we balance the geological instability with the desire to not use coal or other chemical fuels that increase the carbon load on our atmosphere” and this is a “we have the technology, but don’t have the money, do we have the understanding” they are trying to balance all these different things. It always reminds me of Dante, just to bring in things from left field, he said the root of sin is not understanding the consequences of our actions and you have to wonder if the root of doing bad to our planet is not understanding all the scientific implications at work.
Fraser: Its amazing we’re still dealing with the implications of this discovery and I think that is just a short form of how to unleash this whole complex constellation of ideas all at the same time that it’s about death and it’s about WWII and it’s about the power and the risks and Fukushima and all of these things, all at the same time
Pamela: And it’s also about life, it’s about stars, it’s about origins of the big bang and it’s that dichotomy that as scientists, we always have to be concerned. What is it that we’re discovering? The area of the stars is a nice place to work.
Fraser: I think that was great, thank you very much Pamela and we’ll see you next week.
Pamela: My pleasure Fraser.
This transcript is not an exact match to the audio file. It has been edited for clarity.

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