It was *you* doing all trash talking and insisting on a mathematical description of pressure in a vacuum.
Well, no. What I insisted on was a universal definition of pressure.
The moment I handed you a valid option, you got all huffy and puffy and refused to consider it.
I did consider it. And I told you why, in detail, it was awkward and pointless, starting with the fact that relativistic mass is an outdated and redundant concept. All you did was change the calculation from one in terms of energy to one in terms of relativistic mass, which is redundant with energy. So although the two versions were formally equivalent, I detailed why your form was inferior for performing actual calculations. You did not actually contest that.
It is not "pointless" or "stupid" if we're talking about the "pressure" of a "vacuum".
Sure it is. Relativistic mass is redundant with energy. In most situations it's easier to work with energy directly rather than with relativistic mass.
What was "pointless and stupid" was comparing a vacuum to "liquids".
Oh, but I'm
not comparing them. I'm using liquids to demonstrate that you have
no clue about what pressure actually means.
The only reason you balked at my suggestions is that it becomes clear that with no mass, you have no pressure.
Oh, is
that what you thought you were doing? Sorry, I really didn't think you'd be so clueless, but I guess I should have known better by now. Well, this is rather obviously wrong, because you've confused rest mass with relativistic mass (one of the reasons I prefer not to ever use relativistic mass). Radiation pressure is the perfect counter-example: no rest mass, plenty of relativistic mass, and you get pressure. So apparently you didn't even have a clue about what your substitution meant.
The QM issue is *directly related to a persistent, all pervasive EM fields in the vacuum and the carrier particles for the EM field. It is a *force*, not a "pressure"
A force that's applied over an area, and that force is proportional to the area that it's applied over. Divide out that area, and you get a constant, which is...
(wait for it)...
Pressure!
Who'da thunk? As those intro textbooks repeatedly point out, pressure is force per area. So the EM field is indeed applying a pressure. And whether you want to consider ordinary radiation pressure or the Casimir effect, you CANNOT substitute mass for energy in my pressure equation unless you use relativistic mass. But the EM field can (and does) indeed have relativistic mass, so your contention that my definition of pressure leads to zero pressure for a vacuum is wrong.
There is no such thing a "negative pressure".
Once again, yes there is. Whether or not a
vacuum can support negative pressures is a different question, but negative pressures are absolutely real. Again, liquids. Yes, yes, liquids aren't the same thing as vacuums, but your repeated failure to understand that liquids can have negative pressure demonstrates that
you don't know what pressure is.
You folks still have not acknowledged that the Casimir *force* is a *force* that is unrelated to "pressure".
It's a force applied over an area. Divide out that area, and what do you get? A pressure. Seems pretty obviously related to me. And my intro physics textbook says the same thing. In fact, when calculating the pressure of a liquid at depth, it starts out with calculating a force, then derives the pressure from that.
Really, Michael. Don't bother trying to figure out the quantum mechanics of all this. You're still hopelessly clueless about what pressure means, even in a Newtonian context.