George Jones

On 11/05/2024 at 08:59, George Jones said:

Sorry, but I think that this is a terrible resource. I only have had a look at a small portion of the spreadsheet, but I have found mistakes in 3 cells. When these mistakes are corrected, these 3 cells all take on the same value, which is a value that some other cells already have.

In the temperature part of Henry K.O. Norman's spreadsheet (which I have attached), the corrections changed the temperature values in 3 cells to 1.234E-08.

On 12/05/2024 at 13:51, Anton Viola said:

Looking forward to your feedback! Started checking the formulaes and references myself as well.

I have since looked at another of Norman's expressions for temperature, 10²⁶M⁻¹K. In line  82, Norman writes "(10) Hawking’s 1975 paper, his second temperature guess (the factor 10²⁶ is nowhere explained)."

Hawking published his 1975 paper in a high-level mathematical physics journal, and the reader is expected to be able to supply easy (for the research physicists that read this journal) results, such as the 10²⁶ factor. In the last paragraph of the third page of this paper, Hawking writes "In ordinary units this temperature is of the order of 10²⁶M⁻¹K ". In the next sentence he writes "solar mass (10³³g )". Consequently, "ordinary units" means cgs units (centimetre, gram, second), not mks units (metre, kilogram, second).

Once the correct units are used, it is fairly straightforward to derive the 10²⁶ factor. See my attached pdf for details.

Hawking SGL 0.pdf Black Hole Properties Norman.xlsx

On 09/05/2024 at 11:22, Anton Viola said:

Well, took a few steps back and investigated theory/equations about black holes. Found an excellent resource (from 2014, but still valid ..?), which shows clearly a lack of consensus (extremely wide spread of the “expert opinions”). Summarised what I found in there attached spreadsheet. Or have I overlooked things?
 

Sorry, but I think that this is a terrible resource. I only have had a look at a small portion of the spreadsheet, but I have found mistakes in 3 cells. When these mistakes are corrected, these 3 cells all take on the same value, which is a value that some other cells already have.

I started to type a detailed mathematical response in a coffee shop, but a friend came in and I didn't finish. Now I have to go home and face the Saturday expectations of my wife.

I, too, love this book. I got my copy many years ago, and I have read it at least twice. Now I want to read it again, but I can't find it. We just renovated our basement, and I have yet to unpack all my books.

2 hours ago, saac said:

Same process in engineering (fluid dynamics) with use of the Navier Stokes equations in analysis of turbulent flow regimes; from what I remember there are no easy analytical solutions (modelled by differential equations then cracked with lots of CPU power). Laminar flow, yes, but that's boring  

Jim 

Wandering off-topic a bit, but the Navier-Stoke situation, for me, is quite interesting. Engineers and physicists are happy to solve Navier-Stokes on a computer, but mathematicians have yet to be convinced that any reasonable solutions to Navier-Stokes exist (as the mathematics of mathematicians). There is $1 million riding on this! Anyone who can prove existence (without even writing down a solution), or who can find an explicit solution, wins a Clay Millennium Prize.

The attitude of hard-nosed physicists and engineers is that mathematicians are too worried about crossing every t and dotting every i.

15 hours ago, vlaiv said:

Important thing to note is that this model does not have equations like we are used to.

It can only be solved by numerical methods / via computer because it is set of differential equations without nice analytical solution.

Observational data is fed into computer program and best fit is produced. This best fit yields certain functions and numerical values for constants that we have as "solution" to the model.

 

Actually the differential equation for the scale factor (the Friedmann equatiion) for Lambda CDM universes has exact solution in terms of elliptic functions.

I saw totality near the north shore of Lake Erie in Canada. I love the corona. This was the second total solar eclipse that I have seen, as I saw one in Oregon in 2017.

I, too, keep mine fully assembled. For the last 8 years I have stored my fully assembled in a shed. I carry it into the back garden and back when needed.

15 hours ago, Moonshed said:

However, they all suffer from the same problem, which is after being fully charged, and even if left completely unused, the battery will, sooner or later, go flat.

These days, can't Auto-Tune be used to fix this?

Several years ago a colleague asked me to write a short homage to physics that emphasized fundamental curiosity-driven physics. Writing to order, I produced the following hyperbolic passage, which my colleague has used several times in presentations.

"Why study and research fundamental physics? Why study curved spacetime and general relativity? Cosmology? Elementary particle physics? One possibly selfish reason for me and many other physicists is "Because it's fun!", but other reasons exist. Science, including non-applied fundamental science, is part of who we are as a species. Fundamental science is as much part of our culture as music, art, and literature. If we lose the desire and ability (possibly through politics) to ask fundamental “Why?” questions of our world, we have failed as humans."

@kurdewiusz, I have largely stopped arguing with people with very non-standard physics views. I had too many bad experiences at Physic Forums, where I was a moderator for years. I will let others here carry the torch.

Okay, I have much more important things to do, like watch the first Saturday of Premier League football.

@kurdewiusz, in your opinion, is the Friedmann (differential) equation of standard cosmology correct?

18 hours ago, andrew s said:

Pops, bangs, unintended explosions and the odd rogue projectile enlivened the day.

Or intended (by the student!), as happened several years ago while I was teaching a second-year electricity and magnetism lab that involved capacitors. A student took hold of a capacitor and motioned like he was going stick the cap's leads into an electrical outlet. I said "Don't do that; it will explode!".  After I went to help another group of students, I heard a "Pop!" behind me. The student had taped a capacitor to the end of a plastic ruler with leads sticking out, and then had inserted the leads into the electrical outlet.

15 hours ago, Hans Joakim said:

I picked up Sean Carrolls introductory book last year (https://www.amazon.co.uk/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/ref=sr_1_1?crid=1W91PXBQ3JB0P&keywords=sean+carroll+general+relativity&qid=1691008661&sprefix=Carroll+genera%2Caps%2C114&sr=8-1), which I think is great and an easier read than what we had! I’ve also been following these lecture recordings, based on the same book (the whole lecture series is up on YouTube):

I really love this beautiful book, and I bought my copy shortly after it was published, but I don't think that this is quite what @cloudsweeper wants, given that he wrote

15 hours ago, cloudsweeper said:

From my engineering degree, I have even been able to figure out some of the maths of special relativity, but general relativity is on a wholly different plane!  Reckon I'll keep that on a descriptive level, starting from the Equivalence Principle.

Absolutely fascinating, counter-intuitive stuff!

and given that the YouTube lecture course in meant for folks who want a well-motivated but advanced course, i.e., "8.962 is MIT’s graduate course in general relativity, which covers the basic principles of Einstein’s general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology."

More appropriate might be a recent book by Sean Carroll, "The Biggest Ideas in the Universe: Space, Time, and Motion".  This book has a lot prose, but does use a few equations. Carroll attempts to explain what equations mean without giving the reader facility to calculate with equations. Carroll explains this in more detail in the book's Introduction, which can be read using Amazon's Look Inside feature.

Roger Penrose, who has a Ph.D. in pure maths, and who won a Nobel Prize for applying pure maths to black hole physics, recommends the following technique for dealing with lines of equations

On 28/07/2023 at 13:08, ollypenrice said:

Can maths not describe anything which is consistent?  If it can, is there really anything more to the ability of maths to describe nature than that nature is consistent?

I am going to flip this around somewhat. If logic is a branch of mathematics, how is it possible to define "consistent" without mathematics? 😁

Our (cosmological) universe does not have time symmetry, but it does have 6 spatial symmetries. At any instant of cosmological time, there is a 3-dimensional space that, roughly, is symmetrical for all spatial rotations and all spatial translations. This is true even when the 3-dimensional spaces are curved.

On 26/06/2023 at 15:32, saac said:

I wonder if we are like stem cells, starting off with equal potential for either of the related disciplines. Given that maths is so central I wonder what factors  are determinant in our choices.  I guess it's how we see the world that largely influences our motivations. I do find it hard to understand though why pure maths would be followed rather than applied maths or the physical sciences/engineering. Thinking about it now, that is probably due to the bias in my own motivation,  but when and where does it start.?

I guess it's different strokes for different strokes for different folks. If when at university I had been forced to major in something other than physics, I would have chosen pure maths, not one of the more obvious choices, e.g., engineering or chemistry. Engineering and chemistry are both great programs, and I expect that many people, if put in my hypothetical situation, would have chosen one of them.

My love affair with pure maths started when I was exposed to Euclidean geometry in high school, and has yet to end. I took longer than normal to do my physics B.Sc. so that I could take courses in pure math for which there was no room in a standard physics program. I currently am on the thesis-examination committee of an M.Sc. student in pure maths.

On 13/03/2023 at 13:14, Macavity said:

On a lighter note, maybe they should teach some "Maths for Physics Students"?
At least where I was concerned, there was a fair gap, between the 1st Deg level
and the sort of *Matrix Algebra* expected of the more "Theoretical" Physicists.
Maybe this slightly more user-friendly (less combative?) style could be useful...
Something as "simple" as e.g. https://en.wikipedia.org/wiki/Einstein_notation 😬

The 4-year physics B.Sc. that I took in Canada 4 decades ago had many, many math courses as required courses. No math courses were required for the Ph.D., although I did take several.

12 hours ago, iantaylor2uk said:

I have a great book "Mathematical Methods of Physics" by Jon Matthews & R.L. Walker which is well worth getting if you can find a copy.

This was on the reading list for one of my undergrad courses. Interesting passage from its Preface "The course from which this text evolved was originally based on lectures By Professor R.P. Feynman at Cornell University."

How is this different from electrons that strike a detector?

Here is an interpretation of the HUP that I like. Prepare a large number, say 2N, of systems (e.g., electrons) that are in identical states. Measure the position of the electrons in half (i.e., N) of the systems. and measure the momenta of the electrons in the other N systems. Even though all the electrons are in identical states, the measured positions of the electrons will not all be same, i.e., there will be a statistical spread (standard deviation) of the measured positions. Similarly, there will be a statistical spread  for the measured momenta. The product of these statistical spreads will satisfy the HUP. Note that on any single system only one measurement is made. In this interpretation there is no system on which both position and momentum measurements are made.

2 hours ago, VirgoCluster25 said:

I was also taught it was expanding at the speed of light.

Where were you taught this? This isn't correct; the universe is, in some sense, expanding faster than the speed of light 😁. The expansion of the universe is governed by general relativity, and general relativity can be munch more non-intuitive than special relativity!

On 31/03/2023 at 01:36, markse68 said:

stumbled upon this delightful old demonstration of the Stern Gerlach experiment from 1967 on youtube. It’s quite something to see the real apparatus rather than a graphic and I feel I understand its significance a lot better now. An essential tool for investigating “spooky action at a distance” and Bell’s theorem.

Nice.

Interestingly for such a fundamental important result, more than 100 years passed before the original 1922 German publication (1:45 of video) was translated into English.

https://arxiv.org/abs/2301.11343

(Full pdf at upper right.)

17 hours ago, Ouroboros said:

What a lovely film and a very nice demonstration. Good  to see an old experimental rig too.  I’m old enough to remember using chart recorders to capture data. 🙂  thanks for the link. 

I too am old enough. As a student I used chart recorders in physics labs.

Welcome to SGL.

19 minutes ago, PennyRiver said:

+  In a given area of the universe, carve out an imaginary sphere.

+  Calculate the mass of the sphere.

+  Calculate the mass of everything within the sphere.

Sorry, but I am not sure what you mean by this.

I have had a chance to look at this in more detail. Looks good to me; you have clearly laid out your steps.. I worked the example independently, and I get the same result. I got a symbolic expression for Delta M, and then plugged in all the numbers at the end.

Not sure if this is of any interest, but 0.4343 is 1/(ln10), and is involved in the conversion from log base 10 to nature logs. The error in a ln is easy to approximate using a derivative.

What are you given the error in? Apparent magnitude? Absolute magnitude? Distance modulus? Something else?

What are you trying to calculate the error in? Apparent magnitude? Absolute magnitude? Distance modulus? Something else?

9 hours ago, badhex said:

When I break it up, I get 0.02817435337 which I'm sure cannot be correct, it's smaller than the original magnitude error.

In this case, did you forget to take the final square root?

On 16/02/2023 at 12:13, 900SL said:

Can somebody explain why that article states that the photons on the early universe had high kinetic energy and momentum? I always thought (A level physics) that photons were massless

Yes, the rest mass of a photon is zeoro

On 16/02/2023 at 12:13, 900SL said:

and KE was 1/2mV2.

This is (approx) true only for non-relativistic physics.

Another way to @vlaiv's final equation. The world's most well-known equation, E =mc^2, is a special case of a more general equation (my favourite physics equation),

E^2 - (cp)^2 = (mc^2)^2,

where E is the total energy of the "particle", m is the rest mass of he particle, and p is the momentum of the particle.

Suppose that a particle with non-zero rest mass m is at rest, so that its momentum p is zero. The equation then is E^2  = (mc^2)^2, which, after taking square roots on both sides, gives the famous E =mc^2. E =mc^2 is true for particles that have non-zero m, and that are at rest. E =mc^2 is not true for any moving particles.

Now consider the case of a particle that has zero energy E, and has zero rest mass m, e.g., a photon. Then E^2 - (cp)^2 = (mc^2)^2 becomes E = cp.