What does E=MC2 really mean?
Did you know that Einstein's most famous equation didn't actually originate with Einstein?
We're all taught this simple equation even as children and we're told that Einstein did it.
But he didn't in fact, Einstein never published a single paper about it.
Where does it come from?
Well as it turns out, Einstein's paper on Mass / Energy equivalency never featured that equation.
What Einstein actually said is that Mass = Energy/The square of the speed of light.
M=E/C2
These are similar, but mean different things.
The meaning under Einstein's formulation is that as you add energy to a system it gains mass, because mass is a property of energy.
When you say E=MC2 you are describing how much energy is pent up as "rest mass",should you decide to release that energy.
The net effect is that the other energy in the system is ignored. Thus it feels counter intuitive when we go to measure an object at rest and we discover that it weighs less than it's constituent atoms. Yet things like a wound up clock on an express train will weigh more than their atoms.
So when we say E=MC2 it's because we like to think in terms of matter, which under quantum field theory is a form of potential energy, but when we do this, it causes us to forget the simple truth.
Energy is what actually exists. It exists in various forms and mass is just another one of it's properties.
Nice post. I however don't totally agree with one sentence. Mass is not really a property of energy. It is a form of energy itself. At the microscopic level, there are only three forms of energy: mass, kinetic energy and potential energy (which is different from the mass energy). And all of these must be accounted for. When you state that an atom mass is smaller than the sum of the mass of its constituents, what you actually mean is that the atom mass is the sum of both the masses of its constituents and the binding energy.
I would also like to add that E = mc^2 can be generalized to E^2 = m^2c^4 + p^2 c^2 in the case where the particle is not at rest. This holds both for massive and massless particles. (p is the particle momentum)
@lemouth Fair enough, all generalizations are of course going to be faulty.
You're correct of course.
But what I mean by "property" in this context, is that it is something you need to account for when thinking about object = energy.
Let me put it another way.
When you think about a coin (energy), there are heads and tails.
And that's all anyone ever thinks about.
In reality the coin has 3 properties, heads(potential), tails(kinetic), edge(binding) (not going to get started here on spin etc).
Coin as energy, this is what I mean by properties. A better more accurate description would be the collective excitation states of the various fields involved. But this felt like a good way to break frame and it's accurate enough to get people 99% of the way to the most correct answer, beyond which it can get really complicated. :D
Thanks for your comments!
Sure. If you start to be too accurate you will loose everybody. I was only trying to be in the middle (without offensing you of course) :p
@lemouth Nope you'll never offend me by providing corrected information.
Especially if you can cite a peer reviewed reputable source for it.
Remember, this place has real Quantum Physicists, Theoretical Physicists, Mathematicians and even arm chair quarterbacking polyglot nerds like me.
I think we can do an ELI5 on it and get more minds intrigued and excited. While at the same time keeping some solid standards of rigeur.
@lemouth Cool! Sounds excellent! We really do need more people who spend their lives doing this.
Great to meet you!
In this case, I think that confirmation can be found in many quantum mechanics textbooks (I however cannot point you to a given one and a given page number right now as I don't have them with me).
Btw, this is exactly how I introduced the microscopic world to my students when I had to lecture quantum mechanics. That's actually part of my lecture #1 where I mix the scope of quantum mechanics, some description of the microscopic world and some history of science.
@lemouth Oh yeah. Sorry I wasn't saying you needed to cite something that's common knowledge. I was saying I have a tendency to parrot things I've learned once I've learned them. However the scientific world moves so quickly that entire fields of study can crop up, take over the world and then be found to have no basis in reality faster than I can ever hope to keep up.
Hence if I'm wrong especially about something edgy or "wooish". I love knowing as soon as possible. If that information comes from peer reviewed articles, then that's even better.
So remind me, what do you teach again? Because I have some QM stuff that I'm not sure if it's woo or bs, or accepted and valid fact. But whatever it is it's fascinating and got my attention like a bloodhound on a scent.
Eitherway I don't have an audience before I present it and if you have the background for it, I would love to have a sanity check before I run with it much further.
I am answering here as I cannot answer to your answer. During the last ten years, I designed lectures on quantum mechanics, particle physics, the electroweak theory, wave mechanics, electromagnetism, high-energy physics tools, supersymmetry, etc.
My main field of expertise is actually theoretical particle physics.
it mean.. you MATTER!
unless you multiply by the speed of light squared in which case: you ENERGY!
This episode was great @williambanks, We need have discussion about dyson sphere
@jasonmcz The Berenstein Bears are my next topic. i just did Dyson Swarms a couple weeks ago. I believe we found one around Tabby's Star. At this point, to my mind the evidence is just too strong on the pro side for that, until I can see something much stronger on the anti-side, besides "it's never aliens".
These guys are 20ly away from us, it could very well be aliens considering the sheer number of solar systems with planets that could harbor life. And that number becomes all but infinite if you assume that life is any information which takes action to preserve it's own order against entropy.
FYI I am planning to unify all of this and give you guys something mind blowing to think about. But I have to build it up layer by layer. Partly because I'm not sure if I'm right, I'm crazy or in a superposition of both states :D
I love seeing physicists exchange opinions!
I find it fascinating that mathematically speaking, the 2 equations pretty much mean the same thing. That is, in either one, you can plug a number in and get the same result, regardless of what equation you use.
However, intellectually speaking, they are talking about different things. It makes me wonder. There are a thousand equations that describe something in the Universe. If we were to move things around in those equations (as you presented here), what intellectual leaps could we make regarding the Universe's secrets?
@casandrarose You read my mind! I just tracked down this video. It does an excellent job of explaining what happens when we move those equations around.
great to see e=mc2 expressed as m= e/c2.
refreshing way to model this!
I owe you.
@talyvale Thanks! I'm glad you enjoyed it!
One other thing I didn't mention because it's a lot to take in.
Time dilation is a result of m=e/c2
What is happening is that when you move, you are trading momentum through time for momentum through space. The faster you move through space the slower you move through time and vice versa.
Momentum is just kinetic energy meaning that this is the same inertia effect that you feel when traveling at a high rate of speed in a car.
This is also why you can't break the speed of light.
Because you as you approach the speed of light, the amount of total energy in the system means that the ratio of e/c2 begins to approach 1:1 meaning that the total mass also increases towards the planck energy and this would of course be reflected as an increase in the total gravitational field strength of the system.
In effect, any object with rest mass that got close enough to the speed of light would collapse into a blackhole.
Light is composed of photons which are really just discretized packets of EM field radiation, which is purely kinetic energy. However if you could trap enough light you would be able to collapse it into a blackhole.
Taking particles which are entangled and trapping enough partners from each pair in order to trigger collapse into two black holes, should create a stable worm hole. But as soon as you released the trap you would have the mouths of each side take off in opposite directions at the speed of light. Likely doing serious damage to the lab that created it. Not to mention the solar system the lab was sitting in.
This is one proposed design for a hypercomputer (a type of computer predicted to be beyond quantum computing, since it would naturally compute inside of a closed time like curve, especially if you could bring the mouths back together and manage to counter their mutual gravitation).
I should mention the above information doesn't quite sit right with me. I'm parroting something I read and found fascinating. The source if I recall correctly was based on work by Leonard Susskind, but I'm having difficulty finding it on Arxiv now.
Will upvote anyone that finds it. It was entitled something like "Wormhole Hypercomputing".
Is this the paper you mention: https://arxiv.org/abs/1402.5674. I unfortunately haven't read it.
@lemouth Ok this is GREAT! And it's by Susskind. But this is not the one I'm talking about. However it is much newer so I'm going to check this out.
The one I was talking about was circa 2010 to 2012.
He and someone else were discussing the possibility of constructing an ARNN from a wormhole because a paper circa 1997 was discussing that one could compute the whole universe with a hypercomputer capable of computing reals.
The underlaying message was that a classical computer which had a receiver on one side and transmitter on the other, could calculate reals to arbitrary precision as long as the wormhole remained open with one mouth in the past and one in the future. Simply by sending the result of each computation to itself in the past.
Although with his latest paper it looks like Susskind has bought into "the whole multiverse is made of wormholes" camp. So I dunno. I'm skeptical.
I do recall the paper mentioning intentional blackhole collapse via huge EM fields, then when the fields were released. The two mouths taking off at light speed in opposite directions and "spelling possible trouble for the lab, and certain doom for the solar system it was situated in".
That was insightful. Another thing I am thinking about, which is a bit off topic. You could probably guess that it is about #payitforward.
Thing is I do a lot of thinking about posts that I read, and am sometimes inspired by them. So I will be inserting some links at the end of my articles about stuff that is undervalued (in my opinion) and has something to do with the article. Or doesn't. For now it is going to be something relevant and something irrelevant.
Just thought I would share it with you, and maybe get some feedback on idea.
@xanoxt Thanks! Yes the point of #payitforward is to explicitly say "feel free to bring good content, even if that content is your own or someone else's". So adding a list of inspirational material would only be a good thing.
Thanks for this @williambanks!
Upvoted and followed!
One question that always struck me from the first time I started breaking this formula apart in Physics was in regards to the sums of the equation .. for instance:
sum.Energy = sum.Mass * speed.Light ^ 2If its true on the singular instance, I reasoned it should be the same universally. But, since the universe is accelerating, there should be a corresponding increase of mass on the other side of the equation since light speed is a constant.
Is this too much of a gross oversimplification?
@blakemiles84
Well here we have firmly entered the world of spherical cows in a vacuum.
In order to prevent the Universe from collapsing, Einstein added an adhoc term to his original paper on General Relativity.
This term was called Lambda
He added this but when Hubble published his results indicating the Universe was expanding, Einstein retracted it calling it his greatest blunder.
This term is literally the vacuum energy constant of the Universe and right now, whatever it is it seems to be the dominant form of energy in the universe.
There are as many theories about what the hell this is, as there are people thinking about it.
We know it only by it's effects.
It's not pushing things in the Universe further apart, it is the Universe stretching in regions of low mass while gravity dominates in regions of higher mass.
One theory and it's the one that I subscribe to for no other reason than all the cool kids are doing it is this...
The the smallest scales the Universe can be thought of as "foamy". In this quantum foam, a lot of activity is happening, including virtual particles popping in and out of existence. Literally anything but most common would be charged particles which then instantly annhiliate eachother.
This annihilation leaves residual energy in it's wake. The energy doesn't last for long, but it stretches the universe out just a little more. When that occurs, there is suddenly a little more space for these events to occur in, so they occur more frequently. This feeds a cycle and there you are.
I don't find this satisfying, but it is exactly the same process as hawking radiation and it satisfies my inner urge to discretize the universe at the scale of quantum foam.
I have serious doubts that this constant is actually constant.
There is a competing theory which has almost no traction or support, but which states that what we perceive as accelerated expansion is the evolution of time into a space like dimension and space into a time like dimension. The result of dimensional folding. This one satisfies my urge to say that time in general is not constant and instead has a certain fluidity to it, that I don't have an appropriate term or the ability to describe at the moment.
This would actually be a great question for @lemouth since he actually is a Quantum Physicist and is probably much more up to date on what the science is telling us in this regard.
Excellent response. @lemouth -- would love to read that! Following you both, now.
I hadn't heard of the 'quantum foam' concept, but I think I can visualize it.
One theory that I've read that resonates is gravity as an omni-directional, collisionless pushing force that gives all matter, particles, and anything its spin. According to this theory, the pull towards bodies of mass is a result of the dense formations of matter 'slowing down' or 'squeezing' the 'gravitational pushing force' slower than where it is coming from any other direction.
So, how this ties in, when the gravity force is hitting the edge of the universe, its spinning matter into existence when it reaches the whatever nothingness (or literally no thing) beyond the edge of time and space. This would account for the accelerating expansion AND the increase of mass to Einsteins equation.
There are some other very interesting components to this theory as well. The pushing force is what gives light its waves and particles signature, but also its 'speed limit', since light is flowing within a stream of gravity like a leaf down a river.
I can't honestly remember where the hell I read that, but I liked it. I'm not trained in physics beyond undergrad stuff, so I'm sure there are a number of things wrong with it. However, it resonated and it helped me to understand a number of concepts much easier in physics.
@blakemiles84 im sorry but i didnt see a response from @lemouth on it so im not sure what explanation youre referring to. As for my own, The quantum foam theory is one of those that a number of years ago gained a lot of traction but has been dying down as of late.
What would C2=M/E mean then?
Ok, bit of of a misnomer.
C is NOT the speed of light. C just happens to be the same speed at which light travels in a vacuum.
The C in this equation is much better thought of as "Causality".
C is really a measure of speed (d/t) equal to covering 1 planck length in 1 planck unit of time.
It's essentially the framerate of the universe, if like me you think of the Universe in terms of computation.
If you think of space and time as being discretized then C is exactly = 1.
So when you say C2 = M/E you are saying that mass and energy must add up to C2 which is 1 squared when everything is taken as planck units.
Another way of saying it, is that massless energy such as photons, will always travel at C.
So C = 1, then einstein could have written E = M period. Or if C is a constant, then he could have written
E = MK.
He was explaining an inertial effect. Exchanging momentum through time for momentum through space and vice versa. You need to add a concept of rate of change for that to work.
In thermodynamics, the first law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed. Energy cannot be created nor destroy.
https://steemit.com/science/@echoesinthemind/god
I would love some feedback on my post. Specially if you disagree with it. (:
'in an isolated system' entropy, not perpetual .
infinitely open, which universe is, perpetual acceptable?!
love the thread and rich feedback.
Energy is the what allows change to happen in both isolated and perpetual systems.