31–40 of 78 posts
Earlier quoted context omitted.
You can't accelerate anything to the speed of light without an infinite amount of energy. It just takes more and more energy to get closer to that speed. https://en.wikipedia.org/wiki/Speed_of_light#/media/File:Lor...
Does that mean it doesn't take more energy to accelerate an electron to the speed of light than a tennis ball?
Question: is the analogy of thermal energy as particles flying around and bouncing into each other just analogy? At what temperature would the particles fly at the speed of light? > Above about 10^32K, particle energies become so large that gravitational forces between them would become as strong as other fundamental forces according to current theories. I see, the gravitation would become a problem even before the s…
Right, this was how I was taught about temperature, and I'm just realizing now it probably isn't the best analogy... Like, do particles shot through a particle accelerator have a super high temperature? They're moving awfully fast! Or does it have to be "vibration," in which case, "vibrating" relative to what?
Suppose you have a system with 100 degrees of freedom and 2 units of energy, spread out as (0.01, 0.01, ..., 0.01, 1.01). A bunch of its energy is in one of those hundred degrees of freedom. You can assign it two different temperatures: the temperature 0.01, which would describe how energy will right now flow into the system if you connect it to another system with a bunch of degrees of freedom with their own thermal energy (assuming that the 1.01 degree of freedom is "internal" and doesn't interact directly with the outside world), and the temperature 0.02, which would describe how energy will eventually be spread out and hence how it would eventually share freedom with the outside world.
Temperature is ultimately defined in terms of how our uncertainty about the microscopic state a system is in changes as we add energy to that system. The higher this rate of change of uncertainty, the lower the temperature is -- this is why when you connect two systems of different temperatures, in the process of us becoming more uncertain about the fundamental state of the world, energy "spontaneously" flows from the higher temperature to the lower temperature: the certainty gained from stealing energy from the higher-T one is more than compensated by uncertainty created from pouring that same energy into the lower-T one. (In fact there is a family of systems of "negative temperature" which become less uncertain as you add more energy to them: they are "hotter than the hottest possible temperature" because they will gladly give their energy to any "normal" system in the process of us becoming more uncertain about the world.)
The problem is that if we're certain that some degree of freedom has a given amount of energy that's "special", we have a bunch of different definitions of "temperature" depending on how "adding energy to the system" distributes between the "special" degree of freedom and the "thermal" degrees of freedom.
So the usual process is to just totally separate those degrees of freedom as separate systems, the "thermal" ones have a temperature, the "special" ones do not.
Earlier quoted context omitted.
You can't accelerate anything to the speed of light without an infinite amount of energy. It just takes more and more energy to get closer to that speed. https://en.wikipedia.org/wiki/Speed_of_light#/media/File:Lor...
Does that mean it doesn't take more energy to accelerate an electron to the speed of light than a tennis ball?
Ek=mc^2/√(1−(v/c)^2)−mc^2
For vAs v->c it does not matter as much, the lorentz factor is much more significant, the mass operates just as a base multiplier and sum factor.
As v->c, x->0 where Ek~1/x, i.e. tending to infinity with a division by zero when v=c.
In conclusion, the speed is the relevant factor instead of mass when near speed of light, regardless of the object being an electron or the mount Everest.
Of course, assuming the equation holds ;-)
Ooh boy, quantum mechanics is fun :-) Think of the quantum vacuum as having a large number of degrees of freedom waiting to get excited by energy -- like a fleet of unused AWS instances in a system with very effective load balancing. The moment the load (roughly, energy) on the running instances (particle present in the system aka "quanta") increases beyond the threshold for creating a new one (aka rest mass of a new…
Has anyone ever done an experiment to confirm that SR comes into play at ultra-high temperatures?
Looks like they found a way to measure my mix tape
If this were reddit I would've upvoted you, but this kind of cleverness should, if it constitutes the whole post, should be left to reddit. Now, should this thread ultimately hehehe a discussion on the virtues and approaches to creating mixtapes it would be another thing, but at this point in time I'm not seeing this as a positive contribution to discussion. That is why I downvoted your genuinely amusing comment.
Earlier quoted context omitted.
Does that mean it doesn't take more energy to accelerate an electron to the speed of light than a tennis ball?
No hadron can achieve the speed of light. See: Ek=mc^2/√(1−(v/c)^2)−mc^2 For v As v->c it does not matter as much, the lorentz factor is much more significant, the mass operates just as a base multiplier and sum factor. As v->c, x->0 where Ek~1/x, i.e. tending to infinity with a division by zero when v=c. In conclusion, the speed is the relevant factor instead of mass when near speed of light, regardless of the objec…
Earlier quoted context omitted.
You can't accelerate anything to the speed of light without an infinite amount of energy. It just takes more and more energy to get closer to that speed. https://en.wikipedia.org/wiki/Speed_of_light#/media/File:Lor...
Does that mean it doesn't take more energy to accelerate an electron to the speed of light than a tennis ball?