ydoaPs

Can you go into more detail here? What doesn't exist mathematically in QFT? What's the difference between mathematical existence and formal existence?

Ask your friend how they calculated that probability. It's not clear how one would go about getting an answer for several reasons. A huge reason is that we simply don't know what makes something count as life. It's a fuzzy concept (like most) which means there are going to be problem cases. Even for stuff that evolved on Earth this is a problem. Now image somewhere totally alien in every sense of the word. There's no way to be sure that we would even recognize the kinds of life that form elsewhere as life. Though, a big reason to ask is that it's likely fallacious logic being used to calculate this number. It's called Hoyle's "fallacy" for a reason. They assume that atoms just arrange by random chance (as though that's even a meaningful idea) rather than by defined chemical processes. Given the right starting ingredients and the right conditions, the probability of a certain chemical reaction occurring will be precisely 1, but you could calculate it to be infinitessimal using this junkyard tornado reasoning.

Energy is conserved within a frame. What goes in comes out. The total energy is constant. That's not to say, however, that energy is invariant, so you have to be careful. The energy tally can be different for different frames of reference. So, conserved, yes. The same for everyone, no. Is there a specific case you want to discuss?

There are theories that we know are wrong, but we use them because they are good enough in certain (often most) circumstances and are easier to use. We know that GR is less wrong than Newtonian Mechanics, for instance, but we use Newtonian in most cases because the precision increase of going to GR is outweighed by the difficulty cost of going to GR in most cases. On the smaller scale, we have QM vs QFT. They're both attempts to describe the nature of the fundamental constituents of matter and the ways in which they interact, but the latter is consistent with SR and and the former is not. Specifically, in single particle QM, there's a non-zero probability that a particle can travel outside of its light cone. So, basically, why haven't we ditched QM altogether in favor of QFT? In what situations is it preferable use QM instead of QFT and why?

Where, exactly, do you think the metric comes from? [math]R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}+\Lambda{g_{\mu\nu}}=\frac{8\pi{G}}{c^4}T_{\mu\nu}[/math] That [math]g_{\mu\nu}[/math] is the metric. It's a matrix whose diagonal is composed of the coefficients of the distance relation. In this case, the Schwartzchild metric I posted above. As I said, r is the distance of a test particle from the center of the sphere of mass. It's abundantly clear that you don't actually know what GR 'does' given the post I quoted in this post.

The same thing it's always for. From Wikipedia: "In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient gravitational field. According to the Einstein field equation, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid). In the case of test particles in a vacuum solution or electrovacuum solution, this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), spinning test particles may experience additional accelerations due to spin-spin forces.[2]"

No, mordred didn't. r isn't the radius of the massive sphere. It's the test particle's distance from the center of the sphere. Oh? Do tell.

So you can compare apples to apples.

r is the distance from the center of the mass sphere. So, again, I stipulated keeping the test particle in the same spot. rs won't change because Mordred specifically said we're keeping the mass the same.

So, the black hole Earth and the regular Earth will both have a Schwartzchild metric. [math]c^2\tau^2=(1-\frac{r_s}{r})c^2dt^2-(1-\frac{r_s}{r})^{-1}dr^2-r^2(d\theta^2+\sin^{2}\theta{d}\phi^2)[/math] If we're keeping the mass the same, making an Earth black hole rather than an Earth+ black hole, then the metrics will be the same since rs will be the same. Now, you're talking about adding in energy. We're not talking about an Earth black hole anymore. We're talking about an Earth+acraploadofenergy blackhole which has a different rs than Earth. However, that's not what you said when I responded to you saying that it was false. What you said was: That's the Earth blackhole, not the Earth+acraploadofenergy black hole. I maintain that the quoted post is incorrect.

None of that has any bearing on what I said. If you keep the test particle in the same spot, the acceleration will be the same.

No, no I'm not. Thanks for asking, though.

I'm pretty sure that's not true if you keep the center of the Earth and the location of the test particle in the same spots they were before the shrinking.

Well, you need to start with classical physics. Luckily for you, there's been a slew of somewhat rigorous popsci books recently. I'd start with Susskind's "The Theoretical Minimum" along with its companion YouTube series. After that, continue Susskind's series with "Quantum Mechanics: The Theoretical Minimum" and its companion video series. After you've got the basics of QM, and a bit of background knowledge of SR, you can take a look at "Quantum Field Theory for the Gifted Amateur" and Susskind's QFT video series. If you want to get into cosmology, you'll also need to get a basic grip on GR. For that (and, to get the background on SR if you don't have it already), I suggest "A Most Incomprehensible Thing: Notes Towards a Very Gentile Introduction to the Mathematics of Relativity". After getting the basics of QM, you could also go the philosophy route and check out Maudlin's book, "Quantum Nonlocality". Maudlin's also got a great book on spacetime, so after "A Most Incomprehensible Thing", check out "Philosophy of Physics: Space and Time".

It says you're a horrible human being for using IE.

Well, isn't matter-energy in GR just a measure of the 4-momentum? The stress-energy tensor is just the 4-momentum 'flow', yes?

Some people have fans, but in the overall scheme of things it's a small effect. We've done actual statistics and whatnot. Another fun thing that happens is that people will lie about giving neg rep and then complain that someone neg reps them.

I've just checked. No single person has given you negative rep twice. Though, you do have someone suspiciously targeting you for positive rep.

He was supposed to be born sometime this week, but he was born on September 8. That made him very small, so he is unfortunately still in the hospital working on his lungs. I hate to ask for money, but the NICU is very expensive. If anyone feels like helping out with this gofundme, I'd be eternally grateful.

I don't even know what that would mean in reality.

Except, as others and myself have previously pointed out to you, we've done just that. Quantized spacetimes predict that the speed of light will be determined by its energy over cosmological scales. This prediction is well within the sensitivity of our equipment and the discrepancy between c and the predicted value has never been observed even when we were looking for it specifically. We've shown experimentally that spacetime is continuous. And that in no way implies anything is quantized. This is not true. You've been given an example and made a point to say that you saw it. So, now you're just saying things you know aren't true. That's called 'lying'.

Well, the plank time is the time it takes for a photon to cross a plank length. In string theory, there is a relationship between the plank length and the length of a string. The plank length is equal to the fourth root of the coupling constant times the string length: lp=g1/4sls. This means that strongly coupled strings are smaller than the plank length. Thus, the time it takes for a photon to cross that string is less than the plank time. So, if we have a coupling constant of 16, then the time it takes a photon to cross the string is half a plank time. Congratulations, you've seen someone use half a plank time.

Well, I guess it's a good thing that electrons don't orbit in the first place. No. In fact, discrete spacetimes must have variations in the speed of light over cosmological scales. These predicted variations are well within the range of sensitivity of our equipment and this is something that has been tested. Spacetime is not discrete. Yep, it's a proportionality constant. It's also worth pointing out that h alone doesn't make photon energy discrete. That's just an insult to nonsense philosophy.

That's how we got h. It was noticed that light packets come in discrete energy units. No matter what you do, every photon will have its energy proportional to its frequency. The constant of proportionality was given the letter h. It doesn't really have anything to do with units other than choosing units where h=G=c=1 really simplifies many equations. That doesn't mean the units that come from that are in any way fundamental units which cannot be subdivided. As has been pointed out, the plank mass is many orders of magnitude larger than the mass of even the heaviest atom.