Dear Cecil (or anyone else for that matter), I know there is a theoretical limit to the lowest temperature that can be achieved…i.e.: ABSOLUTE ZERO (I say theoretical because, as far as I know, due to quantum theory it can never be truly attained) But what about the limit of heat? Cold is essentially the absence of heat, and heat, as I understand it, is atomic motion (or vibration…I could be wrong), now if, stay with me here…according to Einstein’s theory of Special Relativity nothing can move faster than light, then wouldn’t an atom that begins to vibrate and approach the speed of light eventually reach a finite, albeit REALLY HIGH temperature? I know, I know, matter can’t ever actually reach the speed of light, only energy can, the basic question is still the same…IS THERE A FINITE LIMIT TO THE TEMPERATURE ANYTHING CAN ATTAIN???
P.S. I’ve heard that at the instant of the Big Bang the temperature WAS infinite…but is this just a guess, since we can never really be sure???
Just using my backround in math, logic would say that there is no upper finite temprature based on your assumptions. In math when you are taking a limit where something approches X you never actually reach that point (that point can sometimes be infinite) Similarly in an open set [0,X) you never reach X. In the open set example, for any given Y in [0,X) there is always a point Z in [0,X) such that Y<Z<X. And when taking a limit the same idea applys but we usually think of it in the sense of Y approaches X but never reaches it. Anyways for those reasons (if they make sense) the speed or temprature could never reach a finite temprature because theoretically the atoms can will never reach a top speed.
Isaac Asimov covered this very point in his essay The Height of Up. His conclusion was that there isn’t a theoretical limit to temperature. Temperature is a measure of the average kinetic energy, or mass*velocity, of the atoms or molecules of a material.
As the velocity gets higher and higher and approaches the speed of light in a vacuum, the inertial mass gets bigger and increases without limit. So, by Asimov’s argument, the kinetic energy increases without limit and so does the temperature.
If you raise the temperature high enough, the vibration/motion will overcome whatever force was holding the thing together. If you heat up a solid, it will break the molecular bonds and become liquid, then gas. If you heat up that gas, the electromagnetic force holding the electrons to the nucleai will break up and you have a plasma. The hot plasma will disperse into space unless confined by an external force, such as magnetic fields or gravity. Heat that even further and it becomes more and more difficult to generate this external force. So there are obvious practical limitations. There is a lot of research in this, because if you can confine a high enough temperature plasma it will start to undergo nuclear fusion. But we still can’t match the conditions of the interior of the sun.
Cool your jets, perez (baDOOM ksssh). Cecil already covered this. Some of his statements may have been made obsolete by later advances in theoretical physics, but it’s a damn good effort.
Yup. Asimov overlooked the collapse of particles into black holes when the mass exceeds a certain point. Asimov can be excused because he was a bio-chemist and not a theoretical physicist. My excuse is that I really don’t know all that much.
So did I, and I’m still a bit skeptical. If you just look at one particle travelling in vacuum, its kinetic energy obviously depends on your frame of reference. Can something be a black hole in one rest frame but an ordinary particle in another? How does that work?
I asked this (well, something similar) to my high school physics teacher. He said that the only limit is that nothing can be hotter than the hottest thing in the universe. Of course, this begs the question, how did that thing get hotter than what came before it…
Oh yeah, and welcome to the board. Good question to start with. Just a note: Cecil rarely answers these questions, but there are pleanty of people here qualified to answer pretty much any question you could ever have.
This is a good point. It can’t be the kinetic energy that’s relevant. It must be the interaction energy. So, “each particle becomes its own black hole” is a bit of an oversimplification. What Cecil really meant, I’m sure, was that each point in space becomes a singularity because of all the energy that is concentrated there. The Universe would undergo a phase transition to this new state, which cannot be described without a quantum theory of gravity, as Cecil said.
Well, here’s what the eminent physicist Professor John Baez says:
I don’t pretend to understand this but if Professor Baez says there is no upper limit then I’m afraid I’ll have to take his word for it regardless of what Cecil says.
You could, in principle, make a cloud of gas into a black hole by increasing the temperature, keeping volume constant. Mass is, roughly, that portion of the energy which can’t be transformed away by going into a different reference frame. If you go into the reference frame of any single particle in a hot gas, then the rest of the particles will be travelling faster, on average, so the energy would increase. Thermal energy, then, can be considered a part of the mass.
However, one can get around this by just decreasing the density. High temperatures do not necessarily mean large energies: The corona of the Sun, for instance, is at a temperature of millions of degrees, but it’s sparse enough that you’d freeze to death in it faster than you’d cook.