I think he is talking about conversion of m to E and E to m. Actually he should have written m = E/c^2.
Ah I see, possibly. Well we see both occurring, don't we, for example in the "mass defect" we see when comparing atomic masses. Let's see if he comes back on this.
Energy isn't a thing we measure, right? Here's a thought: erasing information (overwriting it) involves energy, the information is erased because it dissipates to the environment as heat. We can measure how much information is erased over time in some computational process, but the energy involved is 'entangled with' the environment. Okey dokey?
This sounds like dodgy thermodynamics to me. Energy, while not a thing, is a property we can measure, if only relative to some arbitrary datum level. Information is not energy. If by "information" you mean "order", then information is a sort of inverse of entropy, which has units not of energy but energy per unit temperature. There is a concept of "information entropy", which is not something I know much about, save that my understanding is that this cannot be equated with thermodynamic, i.e. S=k lnW, entropy. P.S. Please, for the love of God, don't try to drag sodding entanglement in here as well - unless this is a deliberate wind-up to poor Dan, who appears obsessed by it (along with Minkowski's imagined crimes). Please Register or Log in to view the hidden image!
The division by zero has nothing whatsoever to do with the Lorentz transformations or any proportional math associated with Newton/Einstein's E=mc^2. It has everything to do with using geometry, math, and complex numbers to create invariant intervals out of time as something related to space and from the quadratic beauty of that to conclude that the fastest velocity in the universe has to be the speed of light in a vacuum instead of what really is the case. Entanglement. There's a different thread about what everyone else knows about it and is doing about it. What an observer does is pick a direction in which to observe. How "fast", "slow" do you think they can do that? It is limited by the speed of light only because that's how long it takes for the entangled photons to arrive. If the speed of light does nothing other than to distribute a pair of entangled tin cans and associated length of string, entanglement of the quantum field is what implements the perfectly rigid string necessary to the instant tin can telephone network communication. Kids like me used to play with a pair of those. Not in the 21st century. Your loss. No one here pointed out that you can't physically observe both ends of an EPR wormhole at the same time, either, but that doesn't matter, because unlike relativity, observing one is as good as observing both AT ONCE, in the same instant of time, the eternal and absolute now. That duality seems to be a theme you can't really escape when doing physics. Everything about anything is relative. Thank you all, for the pleasure of both threads. Give it a rest, or carry on, your own choices of directions, speed, and entanglement, of course. Avoid division by zero whenever you can; it is a disconnect unique to proportional math, especially if you haven't a care about whether your beautiful equations have any bindings at all to the physical universe, or consistency, or completeness. This too is a choice of direction.
Information can be defined by the energy required to erase it (see Bennett et al.). I'm afraid sodding entanglement got dragged in there a long time ago Please Register or Log in to view the hidden image!! Preskill briefly discusses entanglement and black holes in a couple of online presentations. The problem appears to us to be related to when the black hole forms and when we can say radiation from the formation becomes entangled with a constant timelike surface. But I'll let John explain it . . .
Then I suppose the idea that the the different resources required to factor a 2048 digit number on a classical or a quantum computer, in terms of space and time, having a connection to the black hole paradox would sound gibber-ish too?
False equivalence. You are citing an example of applied mathematics. The equation reads E = mc^2, which is a theoretical equivalence of values from 2 different perspectives, but is not applicable in RW. If we reverse this becomes ; mc^2 = E . Can we create energy by making matter travel @ c^2 ? From wiki That was the question. As far as I know, matter cannot travel faster than "c", ever! Which prompted the next question of "necessity and sufficiency", to which Danshawen generously offered a very informative link, which explained that sufficiency can be greater, but not lesser than necessity and conversely that necessity can be lesser, but not greater than sufficiency. I still have some thinking to do on this, because if the necessity of E requires a sufficiency of matter travelling at a speed which exceeds "c", I still have some questions. If I say that; all horses = quadrupeds, can I turn this around and say, all quadrupeds = horses? I see the same practical contradiction if we were to reverse the equation of E = mc^2
As the original question was directed at me (but made no sense to me at the time), I will chip in now. You misunderstand the significance of c^2 in E = mc^2. It is simply a conversion constant between mass and energy equivalent. Annihilation of matter and antimatter is one scenario, but so might be e.g. the increased weight of a flywheel spun up via input of rotational KE. Your strange interpretation when swapping RHS with LHS makes so sense relativistically. It's impossible to accelerate matter to speed c, since that would require infinite energy input, thus an infinite relativistic mass (oid school terminology). https://en.wikipedia.org/wiki/Mass_in_special_relativity See esp parts 3 & 6.
Thank you for your reply and link. If I understand it (in context) c^2 is used as a theoretical value, not an actual naturally occurring phenomenon. Can I draw a loose comparison with say, a light-year is not a year of light but a distance (a measurement) over which it would take light a year to traverse ?
No. It's the necessary factor that relates energy and mass equivalent, as demanded by and derived from special relativity. I suggest maybe reading that entire Wiki article, and there is a link at the beginning to another one that may similarly be helpful: https://en.wikipedia.org/wiki/Mass–energy_equivalence That statement is correct but not particularly relevant to your real query. The relation E = mc^2 (and its more general form given in that first Wiki article) has more than ample experimental confirmation.
Thank you all for explaining why the value of c^2 is used in context of the equation, as well as correcting the errors in presenting my thoughts. Please note that I was not trying to dispute the actual equation. I would never presume to try and find a flaw in the theory. I was just trying to find greater understanding of the subject. As promised, I'll just sit back and listen to the discussion. Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
That is a statement about sets. You are saying the set of "horses" lies within the set of "quadrupeds" and - correctly - that that by no means implies that the set of "quadrupeds" lies within the set of "horses". But that is not what an equality sign in mathematics signifies. It signifies that the quantity on the left and the quantity on the right have the same value. As for: "Can we create energy by making matter travel at c²?" , that contains so many misunderstandings it is hard to know where to begin. But I see Q-reeus has responded so I will leave you in his capable and patient hands. I'll just leave you with one related thought about all this: c² has dimensions of L²/T², e.g. square metres per second squared. So it can't be a speed, can it? The dimensions of energy are ML²/T². You can see this from the formula for kinetic energy, E = 1/2 . mv², or the work done in lifting a mass: force x distance, where force is the weight of the mass. By F=ma, the force is mg in this case. So E =mgd. "g" is the acceleration due to gravity, so has dimensions L/T². And we get dimensions of ML²/T² again. Same goes for any other form of energy you can think of. Dimensional analysis is very simple and is one way to lessen the risk of talking out of one's arse.
What I mean is that it seems obvious that the energy required to erase information will depend on the medium by which it is communicated. If it is in a modulated radio signal, the energy required to erase it is zero, surely? The radio wave interacts with a surface and is absorbed. If it is inscribed on a tombstone, it will take quite a lot of energy to erase it, won't it? If it is in a sequence of bases on a DNA molecule, it will take a certain amount of energy, different from either of the above examples, to break the bonds and allow the bases to diffuse away. Also I can't see what can be meant by saying information can be "defined" by the energy required to erase it. Suppose you determine that 2J is required to erase some piece of information. What has been "defined"? As for "radiation becomes entangled with a constant timelike surface", well, all I can say to that is WTF?
This is wandering far off the OP topic but that doesn't seem to ever be a problem at SF so.... 1st para in particular here is worth reading: https://en.wikipedia.org/wiki/Reversible_computing A delicate issue still under active investigation. For a radically different and it seems a far superior approach that at least in the cryptography realm has been successfully demonstrated years ago: http://engineering.tamu.edu/electrical/people/lkish http://www.worldscientific.com/worldscibooks/10.1142/8707 (steep price, but just a read of the tabbed pages is very interesting) http://noise.ece.tamu.edu/Research and Personal Webpages.html Follow the relevant links. As to why that approach hasn't overrun the much more hyped and funded quantum ones - Fashion i.e. Band-wagon effect I suggest.
Well a tombstone is not a "reversible computer", I'll give you that! Please Register or Log in to view the hidden image!
