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I have a vacuum chamber of volume V connected to a vacuum pump via a tube of radius R and length L, and I want to design this "tube" such that R can be controlled in order to provide a constant rate of pressure change inside of the chamber of 2.5 mbar/sec, from atmosphere down to ~0.5mbar...

I've been reading up on the ensemble interpretation (aka statistical interpretation) of QM and it's making a bit more sense to me that it did on the onset, but I still have some questions about how it is consistent with experimental observations of various QM experiments, especially...

Thanks, phyzguy!

Hi PF, I have a setup with two plates that are connected to two different voltages and separated by vacuum. In my case, one plate is set at -10kV, and the other plate is set at -7.5kV. I know the area of these plates, the separation of the plates (which is much smaller than the plate area), and...

In a setup I am designing, I have two conducting plates of similar charge, separated by 1mm of vacuum. The "top" plate, which is mechanically fixed, is charged to -10kV. The other "bottom" plate, which is electrically isolated, but not mechanically fixed (can move toward the "top plate"), is...

I think my diagram was kind of confusing and poorly drawn. AT is supposed to follow that dotted line and represents the light pulse from Earth that reaches the traveler at their destination. OA thus should be 4. BT is the solid line, and is supposed to be a line of constant x' (simultaneity). CT...

Ibix, I think that radar coordinates paper perfectly addresses my issue, thank you for the find! Highly interesting result from the looks of it.

robphy, thank you for the resource, but I don't think that gets at the questions I had with this Paradox. I do fully understand the resolution and how to apply spacetime contraction and Minkowski geometry in order to make sense of the result, I was just confused as to what happens on Earth from...

Ibix, I actually had drawn another diagram where I drew in light pulses, and those definitely helped me make sense of the effect as it was occurring in both frames. I have two such pulses in the diagram above going to and from the point of turnaround of the traveler. Where they intersect with...

I set up a Twin Paradox scenario and accompanying spacetime diagram to help better understand the resolution, but I had a question about the diagram I was hoping someone here could help answer. Please excuse the hastily drawn diagram! (Note: the ' frame corresponds to the outbound trip, the...

Oop, nevermind. Found the correct R expression on wikipedia for radial systems. It is indeed ln(r1/r0)/2πkh https://en.wikipedia.org/wiki/Thermal_resistance#Radial_Systems

I've been using the following equation for thermal resistance to make basic calculations for a few different engineering designs: $$R_t = \frac{L}{kA} $$ Where L is the resistance path length, A is the cross-sectional area perpendicular to this path and k is the thermal conductivity of the...

I think there are ways in theory that you can do it, if you could probe/describe the ergosphere, but from a practical observational standpoint, I know of no way.

1. Time dilation isn't applicable to photons. A gravity well would only effect photon frequency. 2. That is a purely hypothetical effect, and doesn't it say the photons would speed up? Also, it doesn't make much sense to me seeing as pair creation doesn't actually change the speed of light in a...

This is a disappointingly misleading quote from Hawking. There is nothing to stop you from measuring both the position and momentum of a particle, as Hawking seems to imply at first. The HUP states that you cannot simultaneously know both of them at an arbitrary level of accuracy.

Mkbul, don't be surprised that someone falsely told you that black hole singularities collapse into a dimensionless point. This is a very common description of singularities in popular science. It's one I was taught when I was first learning about black holes/astrophysics. In classical...

How would we determine the rotational velocity of a black hole singularity?

HeavyWater, thanks for your clarification. I think I can answer your question by pointing out that εr, your relative permittivity, is defined as the ratio of the capacitance of a capacitor that has the given medium as a dielectric, and the capacitance of that capacitor that with the vacuum as...

I assume you want something capable of reflecting UV light? I don't know of any liquid capable of "generating" any kind of light besides thermal infrared radiation. You would need to input energy, or be burning something.

The second observation makes sense. The first one is counter intuitive. Likely just error, even though repeated a second time. What kind of scale are you using?

I would echo what PeterDonis said about photons playing by different rules. Don't rack your brain trying to figure out how photons propagate. As my professors told me, "photons don't have reference frames". I know this is unsatisfactory, but at the end of the day, photons in a vacuum DO...

Oh, you're right of course. My bad. I was somehow thinking it was a velocity equation and not energy...

Bong_Nebula, that more or less seems correct, as I understand it. These three fields are pretty much joined at the hip.

Simply put, your eV formula only applies for non relativistic electrons. As the electrons become relativistic, the rules change significantly. This is the same reason you can't just look at \frac{1}{2}mv^2 and say "if I put in enough energy, my velocity could exceed c!"

No. Light does not interact with E fields. This is because, as Orodruin said, Maxwell's equations are linear and thus allow for superposition.

Steinein, these are all excellent questions that pretty much anyone who has ever studied SR has asked. They are not at all "retarded". Hopefully I can clarify for you: This is what we call a "thought experiment", obviously because it's not an experiment that could really be performed in real...

Steinein, If a more mathematical derivation of acceleration from the Schwarzschild metric would help you understand how acceleration comes from geodesics in GR, you can find that here: http://mathpages.com/rr/s6-07/6-07.htm It is as simple as setting up the metric (with no angular momentum)...

As far as I understand it, for two distant points in space, like two far off galaxies, unless there is motion between the two relative to the expansion of space, then there is no relative rapidity or velocity between the two. I.e, you wouldn't have a Lorentz boost between their frames.

Thanks guys. Big help.

I know lead is a great shield against gamma particles due to its extraordinary density, but I wonder if it can also block beta particles, or is it transparent to them due to being electrically conductive? Thanks ahead of time for your responses!

The equation is balanced, but would it actually work? NaOCH3 + CO2 + H2O → NaHCO3 + CH4O Or would the reaction simply ignore the water in the left hand side and go, 2NaOCH3 + CO2 → Na2CO3 + H2O + C2H4 Or perhaps a little of both? I'm just starting to teach myself Chemistry, so any insight...

Perfect. Thank you!

I was wondering whether thermonuclear fusion could be achieved in accretion disks around black holes, or even neutron stars/white dwarfs. Seems like, in AGN at the very least, you would easily get the kind of temperatures and pressures necessary for thermonuclear fusion, perhaps even synthesis...

To clarify, I'm not confused as to how massless strings can add up to make massive objects, I understand why that happens. My question has more to do with the speed at which strings move. If strings are massless, they must travel at the speed of light, correct? If so, then first off, what is the...

Thanks, Nugatory! I think this is making more sense to me, now. So am I getting this right? Light does not have a rest mass itself, but it can increase the rest mass of systems it is contained in?

Thanks for the link, Wannabe. I'm actually pretty dismayed that I never learned this in college. When was GR used in this thread?

So if we have two identical boxes, and we fill one of them with light, even though the light has no rest mass, the energy from the light will contribute to the rest mass of the box? I mean I get that it would increase the weight, like, on a scale... How does the box know it is filled with...

:confused: How? What about the potential has a rest mass? The potential is just created by an electric field between the anode and cathode. The electric field is just composed of gauge bosons--photons, so the field is massless, yes? Where does the mass come from?

Wait, but doesn't that equation you have for E2 neglect potential energy? That's just a statement of total energy = kinetic energy + rest energy. Obviously p = 0, so you just have ##E = mc^2## the whole time. But this doesn't make any sense, because you're saying that the energy of the battery...

I didn't say the battery didn't have invariant mass, I said that the chemical/electrical potential which drives the whole system doesn't have invariant mass of which to speak. Just like a gravitational potential doesn't have invariant mass.

Exactly my thoughts... In classical physics, it can't, however, in general relativity, the force of gravity on an object is actually related to its momentum, not its mass, and in special relativity, we learn that momentum is not just simply mass x velocity, but you actually need to throw the...

I mean, I totally understand how this happens in fission reactions, but I am lost as to how you lose mass in a battery. Maybe it's my understanding of how a battery works that fails me...how does losing thermal energy in the circuit take away from the mass of the battery? The energy present in...

These are 10 nanograms of relativistic mass?

I don't believe in relativistic mass. :tongue: Though, I suppose that if the battery IS losing energy, then according to GR, the gravitational force acting on it is lessened, which means that its weight WOULD technically have decreased? Even though its invariant mass (I hate having to add...

No, the thermal energy comes from resistance in the circuit, which dissipates the electrical potential, which is generated from a chemical potential. There is no mass-energy conversion in this system.

That's untrue, the E in E = mc2 is an internal energy, a mass equivalency energy. The chemical potential in a fresh battery is not equivalent to this kind of energy. By this logic, an object would gain mass simply by being raised in a gravitational field...

Look at it this way, if the weight of a battery decreased after being depleted, it would have to mean that the weight of the circuit it was attached to increased. Power this circuit for years with many batteries, and the mass of the circuit would necessarily have to increase arbitrarily. Is this...

Regardless, any changes in weight should be all self contained. If there is weight change in constituent parts, then some parts are gaining mass from other parts, but it should all be conserved.

It would not. Batteries simply convert their chemical potential into electrical potential, when attached to a circuit. They do not lose any mass.

Good to know. Thanks for the advice!