joigus

2 minutes ago, swansont said:

1.5 min was for aerosol. 2 min for surfaces. Typically you look at >5 half-lives for significant reduction. That’s an extra 10 minutes.

That makes sense. Half the viruses is not so good.

2 hours ago, joigus said:

I've found a pedestrian way to do it without looking at tables. If you're not interested, don't pay attention.

What part of this couple of sentences you didn't understand, taeto? I wasn't talking to you when I said it, but anyway, as you seem to care so much...

And sorry for 'patronizing' you. Really.

1 hour ago, taeto said:

The Riemann integral is not defined unless the integrand is defined throughout the integration interval, and this is not the case here.

There are more integrals in this world. Have you ever heard of the Lebesgue measure? I often think of integrals in terms of the Lebesgue measure. The trick is looking at the domain and the range of the function. "The range is infinite" becomes no more worrying than "the domain is infinite." Another name for it is mathematical power. No matter how you want to do it with Riemann, you're gonna have to face the singularities, because those are in the domain. If I've found them with my method, believe me, you're gonna find them too. No integral handbook in the world will get around that. That's a property of the integral, not of my method. I may take a look at how rigorously it is defined with the Lebesgue measure. Maybe Cauchy's theorem. But not now.

Most integrals in QFT are Lebesgue or Cauchy complex, not Riemann. Think just a little bit outside the Riemann box, please.

1 hour ago, taeto said:

It is a mistake when you say "this reduces to".

I said "this reduces to" about the simple algebraic steps, not the convergence arguments.

1 hour ago, taeto said:

So however much I want to believe your solution, I think we should offer yet a better proof.

I honestly think I should go to sleep now, but who knows. I'm finding it difficult lately.

Just now, joigus said:

There are more integrals in this world. Have you ever heard of the Lebesgue measure? I often think of integrals in terms of the Lebesgue measure. The trick is looking at the domain and the range of the function. "The range is infinite" becomes no more worrying than "the domain is infinite." Another name for it is mathematical power. No matter how you want to do it with Riemann, you're gonna have to face the singularities, because those are in the domain. If I've found them with my method, believe me, you're gonna find them too. No integral handbook in the world will get around that. That's a property of the integral, not of my method. I may take a look at how rigorously it is defined with the Lebesgue measure. Maybe Cauchy's theorem. But not now.

Most integrals in QFT are Lebesgue or Cauchy complex, not Riemann. Think just a little bit outside the Riemann box, please.

I said "this reduces to" about the simple algebraic steps, not the convergence arguments.

I honestly think I should go to sleep now, but who knows. I'm finding it difficult lately.

And oh, please, believe you me: If you find an integral with singularities in the domain that has been solved in a handbook. Some mathematician has proven convergence way ahead of the handbook going to press. Same goes for Wolfram or the like.

I've found a pedestrian way to do it without looking at tables. If you're not interested, don't pay attention. First you reorder your integral by taking care of the $r$ part, while factoring the angular part to the left.

You integrate by parts the r factor,

\[\int_{0}^{2\pi}d\varphi \frac{1}{\cos\varphi}\int_{0}^{a}dr r\frac{\partial}{\partial r}\left(\log\left(a+r\cos\varphi\right)\right)\]

1 hour ago, swansont said:

What duration of exposure is necessary?

Swansont, here's a link to recent study I've seen: https://medicalxpress.com/news/2020-04-sunlight-coronavirus-quickly-scientists.html?fbclid=IwAR2ZQLaVm5X1N--fJQit5xyxBzSTHp8Ow4vsUfQsNjLKi7VF0HNpEf_Ys2A

They combine virus in aerosol with high diffusion; as I recall. Humidity is also involved. UV exposure as well. Conditions try to emulate outdoors rather than what Enthalpy suggests for money. But maybe you guys can get something else from it. With all factors together half-life seems to be cut down to 1.5 min. There are separate data with just radiation, just diffusion, just UV, if I remember correctly.

1 minute ago, joigus said:

Swansont, here's a link to recent study I've seen: https://medicalxpress.com/news/2020-04-sunlight-coronavirus-quickly-scientists.html?fbclid=IwAR2ZQLaVm5X1N--fJQit5xyxBzSTHp8Ow4vsUfQsNjLKi7VF0HNpEf_Ys2A

They combine virus in aerosol with high diffusion; as I recall. Humidity is also involved. UV exposure as well. Conditions try to emulate outdoors rather than what Enthalpy suggests for money. But maybe you guys can get something else from it. With all factors together half-life seems to be cut down to 1.5 min. There are separate data with just radiation, just diffusion, just UV, if I remember correctly.

For money disinfection, radiation intensity would be crucial, though, so maybe not so useful this study...

23 hours ago, Zodiac said:

I am sorry but your answer is not good thinking! 

I am sorry but your thinking is not good question!

Not sense make it now, not sense make it ever!

Shut down or up, as you please!

1 hour ago, Markus Hanke said:

One cannot simply assume that accelerating such a mass will automatically lead to collapse; this is actually a very complicated problem, and would have to be treated mathematically to see what would happen. Even accelerating a fully-formed black hole leads to some non-trivial results (see here for example), and a system just about to undergo collapse is far less trivial still (remember we would need to work with interior metrics here).

My intuition is that nothing would happen actually, but I might well be wrong.

Completely agree. That problem calls for numerical GTR.

I was thinking along same lines when I said,

13 hours ago, joigus said:

Whether the system collapses or not would, I suppose, depend on the details of the dynamics. Maybe what you would do is save it from collapse.

On the other hand, linear accelerations for stellar objects are very rare phenomenologically speaking, I surmise. Plus any linear acceleration field would lead to accretion rather that inducing threshold trespassing, my intuition tells me, concurring with you, perhaps.

But there could be an experimental/astrophysical context to do the trick perhaps. A neutron star approached by a heavy stellar interloper which induces strong tidal forces in it, as well as very intense centrifugal potentials. See if any such event of BH formation can be detected. But the acceleration field we're talking about would be very different, of course. 

8 hours ago, MigL said:

I had read about J A Wheeler's Geons ( gravitationally constrained ( non-singular ) EM radiation, but can't seem to find anything by L Susskind on gravitationally collapsed photons with a simple google search.

Thank you for this pointer. I didn't know about geons. I'm very interested in self-consistent classical solutions.

33 minutes ago, MigL said:

I wouldn't think a BH could remain a BH if its mass wasn't equivalent, or greater than    (Rs*c^2)/(2*G).
It doesn't make sense, then again nothing about BHs is common sense.

There are so many speculations about them. You're right. There's nothing common-sense about BHs. I think angular momentum may play a key part and, although Schwarzschild's solution is an exact one, only the Kerr-Newman maybe makes sense, the rotating one.

33 minutes ago, MigL said:

I had read about J A Wheeler's Geons ( gravitationally constrained ( non-singular ) EM radiation, but can't seem to find anything by L Susskind on gravitationally collapsed photons with a simple google search.

It's in one of his video lectures. Don't know where it is though. I'll look it up. The thing about Susskind is he's so intuitive and pictorial. Even in the most abstract and difficult topics. Although he always discusses the Schwazschild solution.

His lectures on supersymmetry, even though he's clearly unhappy at the end, are amazing. SS I think must be correct in some sense we haven't understood. A basic exposition like Susskind's I think is perfect for anybody young, without prejudice, that would like to have a go at a possible re-interpretation. But that's off-topic.

58 minutes ago, MigL said:

Hadn't even noticed the part that involved acceleration; I just assumed it meant a higher speed.

So, assume you have a mass on the verge of gravitational collapse to a BH.
And you accelerate it such that the fields and/or dynamics of the system lead to gravitational collapse.

What happens if you remove the accelerated condition/field geometries/system dynamics ?
Does the BH drop its event horizon, and pop ( very big pop ) back into 'normal' space-time ?
Or does it continue as a BH ?
 

Once it's fallen, there's no way back.That's what the theory says (Hawking radiation aside.) In fact, there is a very, simple, very nice Gedanken experiment explained by Lenny Susskind of a sphere of photons converging to a point, in such a way that a BH is bound to form, but even though you have the illusion that something could be done about it, there is a point past which the photons are doomed. I don't remember the details, but maybe I could find it. But I wouldn't bet my life on what a BH is actually going to do.

On a rather more speculative note, I think gravitational horizons have something very deep to do with the problem of the arrow of time that we haven't understood very well at all.

On 4/29/2020 at 7:29 PM, rjbeery said:

Hi there!

"Black hole creation" is obviously an absolute event at a given point in space-time, and black holes are created when a particular energy density threshold is reached. My problem is that kinetic energy is a relative calculation. If a mass is sufficiently dense to be close to the Schwarzschild radius, and we accelerate it, we can obviously surpass the required density threshold according to our frame.

How does general relativity reconcile this?

 

Very good question. It reminds me a lot of the twins paradox, but for GTR. The solution to the puzzle may go along these lines:

If I understand you correctly, you've got yourself a bunch of matter that's stopped compressing just before it becomes a black hole, but it hasn't. (The Fermi degeneracy pressure is just enough to hold it partially outside of its Schwarzschild horizon.) Then you push it just enough from one side so that its energy density reaches the threshold, and it turns into a black hole. How could that be, if kinetic energy is --allow me to rephrase-- a frame-dependent concept?

That means that if you go to a different inertial frame the kinetic energy, that in the first inertial frame looks like

\[\frac{mc^{2}}{\sqrt{1-v^{2}/c^{2}}}\]

would look like its rest energy

\[mc^{2}\]

Yes, but you've said that you're accelerating it, so there is no inertial frame you can go to where you can see it with constant zero velocity.

In somewhat more technical words, you must include the fields that are accelerating your black-hole wannabe and either include them on the right-hand side of Einstein's equations (if they're other than gravitational) or in the Einstein tensor (if they are more gravitational fields). That's not frame-dependent, but covariant under general coordinate transformations.

\[G μ ν =8 π G( T μ ν + δ T μ ν )\]

Whether the system collapses or not would, I suppose, depend on the details of the dynamics. Maybe what you would do is save it from collapse.

Many paradoxes arise in relativity (both special and general) when you forget that your reasoning requires non-inertial frames in order to make sense.

19 minutes ago, joigus said:

 

but covariant under general coordinate transformations.

\[G μ ν =8 π G( T μ ν + δ T μ ν )\]

 

Covariant means it is a tensor, and if a tensor is zero in one reference frame at a point, it is zero in every reference frame. So your force is not zero in any reference frame.

Feynman Lectures on Physics, volume 1, chapter 1, Section 1-3. Atomic Motion. Go to your local library and start reading Feynman now.

Then start mimicking Feynman in whatever way you can without giving up your principles, and maybe buy a pair of bongos.

Just joking. But the key word in all of this is: Feynman.

15 minutes ago, Moreno said:

https://www.nbcnews.com/think/opinion/iq-rates-are-dropping-many-developed-countries-doesn-t-bode-ncna1008576

As a solution to this problem I can envision accepting as much as possible immigrants from the South of Tropic of Cancer and especially Papuans who are (it is well known) are very talented. What do you think? 

That's probably because they eat their grandpa's brain for supper (true story.) They really are are very talented.

1 hour ago, Area54 said:

I strongly suspect that is not going to be the case in manner which is significant for this discussion. The Himalaya are, as you know, vast and contain a wide - and typical - variety of rock types. Their elevation and associated deep levels of erosion expose that range of rocks. I would be surprised if the deviation was significant. Certainly, the variation could not possibly be sufficient to make a meaningful dent in the CO₂ released by human activity annually, which I understand is the point you are focusing on. Or, were you heading in another directIon?

This very much converges with what I was thinking --even being an absolute nuthead when it comes to geology. The Himalayas are very much geologically active. They are very "plastic," so to speak. Erosion is at its maximum Earth-wise (you just have to take a look at the Kali Gandaki gorge.) I'm sure swathes of relatively young or "uncooked", sedimentary, non-metamorphic rock are being exposed too. But I must confess I'm not sure by any means...

Eons of rock formation are being stripped away there. What do you guys think?

13 hours ago, Scienc said:

Why does the equation τ = -n.R.T.ln⁡ (v_2 / v_1) only work for reversible processes? 

You are, as Endy0816 says, considering the work done by an ideal gas in an isothermal expansion or compression.

Following your notation,

\[\tau=-\int PdV=-\int P\left(V\right)dV\]

So that,

\[\tau=-\int nRT\frac{dV}{V}=-nRT\log\frac{V_{2}}{V_{1}}\]

The reason why that procedure is only valid for reversible processes is that if you want to be able to guarantee that the equation of state \[f\left(P,V,T,n\right)=\frac{PV}{nRT}=\textrm{constant}=1\] is valid throughout the process, it must take place under equilibrium conditions throughout. In other words, the control parameters must vary very slowly compared to the relaxation times of the gas, so that it constantly re-adapts to the "differentially shifted" equilibrium conditions. Those are called "reversible conditions". Chemists use the word "reversible" in a slightly different sense, so be careful if your context is chemistry.

6 hours ago, studiot said:

How would you define T in a non revesible process ?

Exactly.

17 minutes ago, studiot said:

However I would appreciate more information on why you think the Himalaya removes much carbon dioxide, given this description of the principal rock types

I was quasi-quoting Dan Britt in Orbits and Ice Ages: The History of Climate. Conference you can watch on Youtube.

You got me: argument of authority, I should be ashamed of. Conversations with you are starting to get very stimulating. Thank you very much for the references. I'll reconnect in about 5+ hours, then learn geology in about a couple of hours, and then keep talking with you, hopefully.

The bio-data I got mostly from https://www.amazon.com/Life-Science-William-K-Purves/dp/0716798565 and a wonderful MIT course by Penny Chisholm.

On 2/13/2020 at 5:57 AM, drumbo said:

How can we claim that elevated CO2 levels and higher temperatures will lead to the collapse of ecosystems, when under those very conditions the most demanding organisms in terms of caloric requirements were able to thrive?

I understand how you can say that. But it's not that clear to me. First, dinosaurs, like any other megafauna, are almost anecdotal in terms of primary production, carbon cycle, etc. To give you an example, there are about ten trillion tons of methane stored in the oceanic bottoms that can't get out thanks to methane-metabolizing microscopic archaeas that are keeping it at bay. And, mind you, methane is 25 times more greenhouse-effect inducing than CO₂ is. If you want to understand ecosystems you must look at microorganisms. They don't look as pretty in a theme park, but are far more important for the global chemistry.

Another question is the rate at which this is happening. Back in the time of the dinosaurs the conditions were quite stable, and many big animals (quite a big bunch of them in terms of animal biomass) may have been slow-metabolism. As to the dinosaurs, we don't really know if they were or how many there were. We do know that all the plants were C3, because C4 plants did not exist. How did that affect the carbon cycle? Be aware, e.g. that RubisCO, the carbon-fixating molecule, is the most abundant organic molecule on Earth by far.

In fact, C4 plants, which are more efficient at sucking up CO₂ from the atmosphere, precisely evolved to adapt to the new, slowly-changing, low-CO₂ atmospheric conditions. And that's the observation that leads me back to the question of rate. Organisms need time to adapt, measured in tens of millions of years, not decades, for those paradises that you picture in your mind to establish themselves.

We are now pumping into the atmosphere an estimated billion tons of CO₂ per year. The Earth is 100 years within a Milankovitch cycle of glaciation, and yet the glaciers are clearly melting, and fast. We are really fortunate that the Himalayas are still pushing up, because this geological process sucks CO₂ from the atmosphere at an incredible rate, and sends it back to the sea.

The really big question now is what will happen when the ice sheet on Greenland sloshes down to the North Atlantic, as it is sure that the salinity will go down significantly and the conveyor belt that equilibrates the water temperature will eventually stop. It is estimated that that will happen by 100 years' time. Have you thought in any depth about these and other factors?

1 hour ago, studiot said:

No one is disputing the fundamental nature of energy considerations.
[...]

But it is not the only game in town.

I totally agree. In fact, in the topics of physics that are dearest to my heart, it is my conviction that we must overcome this concept.

1 hour ago, studiot said:

Nothing loaded about the word kinetics. Yes it was the first thing that sprang to mind when I mentioned it and I was referring to kinematics, which specifically excludes the causes (force, energy, action etc) of the motions. However I am not sure how energy is involved in the geometry of a random walk in 'the kinetic theory' or and it is not often involved in chemical kinetics, or the calculation of p values, say pH for instance.

I see your point. I went back to my sentence and I think what I meant (or must have, or should have meant) is "The culprit of all this is the fact that thermodynamics always forces you to consider energy."

Instead of,

10 hours ago, joigus said:

The culprit of all this is the fact that physics always forces you to consider energy,

1 hour ago, studiot said:

You may have heard of this delightful book by Mark Levi

The Mathematical Mechanic.

https://books.google.co.uk/books/about/The_Mathematical_Mechanic.html?id=lW5vQK6Tcu8C&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false

Mark has some very interesting ideas about using energy methods.

No, I haven't, but from perusing the first pages --although the energy arguments weren't there--, it looks like a very interesting outlook. It reminds me of what Perelman did to solve the Poincaré conjecture: consider the Ricci flow to prove a topological statement. That's using a physical idea to solve a mathematical problem.

I would talk more about this delightful topic, but my kinetics is forcing me to slow down. Maybe later.

It's been a pleasure.

6 hours ago, MigL said:

P, V, and T are independent variables, and can be considered just like x, y, and z coordinates in math.

1 hour ago, studiot said:

I have to disagree with this.

1 hour ago, studiot said:

So P, V and T are not all independent since they are connected by an equation of state.
Only two of them are.

I have to agree with studiot's disagreement. That's one of the most common obfuscations when studying thermodynamics (TD). In TD you never go outside the surface of state, defined by the equation of state f(P,V,T,n)=0. That's why they most emphatically are not independent variables. This is commonly expressed as the fundamental constraint among the derivatives:

I concur with swansont. Only, I think he meant,

W = - delta(PV) assumes constant P

when he said,

On 4/18/2020 at 1:13 PM, swansont said:

W = -P (delta V) assumes constant T and n 

as W = -P(delta V) is just the definition of work for a P, V, T, n system (the simplest ones.) And when n, T are constant ==> d(PV)=0 ==> W = -pdV = +VdP (for that case in an ideal gas.)

Just to offer a mathematical perspective. If you differentiate (increment) PV=nRT, you get

PdV+VdP = nRdT

(d=your "delta"=increment, small change)

or for varying n,

PdV+VdP = RTdn+nRdT

because, as swansont says, you must know what's changing in your process, and how. You see, in thermodynamics you're always dealing with processes. To be more precise, reversible processes (That doesn't mean you can't do thermodynamic balances for irreversible processes too, which AAMOF you can.). Whenever you write "delta," think "process."  So, as swansont rightly points out, what's changing in that process?

The culprit of all this is the fact that physics always forces you to consider energy, but in thermodynamics, a big part of that energy is getting hidden in your system internally, no matter what you do, in a non-usable way. This is very strongly reflected in the first principle of thermodynamics, which says that the typical ways of exchange of energy for a thermal system (work and heat) cannot themselves be written as the exchange of anything even though, together, they do add up to the exchange of something (here and in what follows, "anything," "something," meaning variables of the thermodynamic state of a system: P, V, T, PV, log(PV/RT), etc.) 

So your work is -PdV, but you can never express it as d(something). We say it's a non-exact differential.

It's a small thing, but not a small change of anything

The other half of the "hidden stuff" problem is heat, which is written as TdS, S being the entropy and T the absolute temperature, but you can never express it as d(something). Again, a non-exact differential. And again,

A small thing, but not a small change of anything

Enthalpy and Gibbs free energy are clever ways to express heat exchange and work as exact differentials, under given constrictions for the thermodynamic variables.

And Helmholtz's free energy is something like the mother of all thermodynamic potentials and its true pride and joy.

8 hours ago, joigus said:

You may be right. Dimensional arguments could work. Let me think about it and get back to you in 6+ hours. I have a busy afternoon.

Thank you!

Yes, taeto, you are right, unless I'm too sleepy to think straight. The thing that's missing in your argument is the transformation matrix, which is, I think, what you mean by,

8 hours ago, taeto said:

This is supposed to be the only tricky part.

I don't know if you're aware of it, but any Gauss reduction operation can be implemented by a square non-singular matrix. A change-of-basis or "reshuffling" matrix. Let's call it D. So that,

AB = ADD^-1B = A'B'

The "indexology" goes like this: (mxn)x(nxm) = (mxn)x(nxn)x(nxn)x(nxm)

The first factor would be an upper-triangular matrix (guaranteed by theorem that I can barely recall) but, as it has fewer columns than rows, at least the lower row must be the zero row, so that the product must have a zero row. Right?

(AAMOF you can do the same trick either by rows on the left or columns on the right; it's one or the other. Then you would have to apply a similar reasoning to B instead of A, you're welcome to fill in the details.)

This is like cracking nuts with my teeth to me, sorry. That's what I meant when I said,

23 hours ago, joigus said:

I don't know whether you're familiar with index notation. If you are, I think I can help you. If you aren't, I can't, because it's just too painful.

But that was a very nice piece of reasoning.

1 minute ago, joigus said:

A change-of-basis or "reshuffling" matrix.

It's actually not a change-of-basis matrix, but a completely different animal.

8 minutes ago, taeto said:

It is perhaps not so clear.

We have a product AB of matrices, where A has more rows than columns.

Suppose that if we perform an elementary row operation on A to produce a new matrix A′, then there is a matrix B′ for which AB=A′B′. (This is supposed to be the only tricky part.) 

Then since by elementary row operations we can bring A into a matrix A¯ that has at least one all-zero row, there will be a matrix B¯ for which AB=A¯B¯, such that the latter matrix has at least one all-zero row. 

Now it follows from the formula for the determinant that A¯B¯,  and therefore AB, has determinant zero.   

You may be right. Dimensional arguments could work. Let me think about it and get back to you in 6+ hours. I have a busy afternoon.

Thank you!

15 hours ago, taeto said:

Can you use Gaussian elimination?

Gaussian elimination does not help here. The reason being that it requires you to reduce your matrix to a triangular form, and in order to do that, you need the actual expression of the matrix, not a generic amn

32 minutes ago, Strange said:

Busy, busy, busy. Places to go, people to illuminate

Nicely put.

I get the impression that some people read books/articles (and answers on forums like this) having decided they are all wrong and just looking for things they can disagree with.

My same impression.

On 1/7/2020 at 9:14 PM, Angelo said:

Space is a constant,

How can a continuum be a constant? Could you elaborate on that? Maybe you're on to something. 

Can a stone be unhappy? See my point?

On 1/7/2020 at 9:14 PM, Angelo said:

There is no absence of gravity where mass is concerned

If there is **one** feature of gravity that singles it out from every other force in the universe is the fact that you can always locally achieve absence of gravity (equivalence principle, EP). The only limit to this is second-order effects, AKA tidal forces. Jump off a window and you'll find out about EP. Get close to a relatively small black hole and you'll find out about tidal forces. Read a good book and you'll find out about how this all adds up. Oh, and mass is not concerned at all in GTR, as it plays no role in the theory. It's all about energy. It's energy that provides the source of the field. What you call mass is just rest energy, and this is no battle of words. Photons of course have no mass because they have no rest energy; and they have no rest energy because... well, they have no rest.

On 1/7/2020 at 8:04 PM, Angelo said:

how relativity which explicitly says that nothing with mass can travel faster than the speed of light

Incorrect: Special Relativity (SR) says nothing (massless or not) can travel faster than the speed of light.

Because GTR says geometry of space-time must locally reduce to SR, things moving locally can't exceed c. In other words: things moving past you can't do so at faster than c. 

People here have been quite eloquent so I won't belabor the point.

I don't want to be completely negative. My advice is: Read some books, with a keen eye on experimental results; then do some thinking; then read some more books; then some more thinking, and so on. Always keep an eye on common sense too. Listen to people who seem to know what they're talking about, ask nicely for inconsistencies and more information, data. Always be skeptic, but don't just be skeptic. It doesn't lead anywhere.