Origins of the Universe

@maxdancona,

I think Ive been talking about my four yar task with writing a combined ( hard back paper and e-based) beginning textbook of geology.

Ive found that, kids who take the program in becoming geologists are , in about 25% of the and almost half do below their academic (SAT projections) and they are often poorly educated in the needs of math that we demand. Consequently Ive been working with a on-staff professor of physics partner on "simplifying AND ENTERTAINIFYING" THE CONCEPTS OF DIFFERENTIL AND INTEGRAL CALCULUS, (from which ALL our understandings in radioisotopes, thermo,rock deformation, stress and strain, and heat flow, erosion patterns, magnetism and gravity) come from. Many schools require beginning text in phys geology called "The Earth"(Turner Verhoogen and Weiss). This text is a scary introduction to physical geology because it assumes a working knowledge of differential equations of higher orders, vector analyses, Integral solcving, expansions, and some pretty fancy statistics (like krigging and variogramming)GOING IN TO THE PROGRAM.

SO weve been working on a text that starts with the very basic explanations they used to use in introductory calc. We go WAAAY back when calculus was mostly used for carpentry, bridge building , and cannon firing, it was, back then, explained in waay less fancy and often abstract terms than "y is a (function) of pi times x"> Such "purely mathematical" explanations of introductory calculus hs scared away many really good students because their own cal introductions in H S were done by teachers who were themselves flummoxed.

Weve gone back to the basics that differential calculus has to do with the division of quantities into teeny parts and that integrl calculus has to do with the addition of these teeny parts into a desired quantity. Everything else is just
1what material we're working with
and
2 the many ways we do it.
My partner has been experimenting with several classes in chemistry, physics and geology where the students appeared to be confused (mostly with the terminology of the calculus and not what they are being asked to do). We are exposing them by using "talk" experiments like measuring mine areas or rock deformation , or the relationships between pressure and temperature .
Weve been detouring to this area and my text has taken a back seat.
I ultimately want to have a program on the math and calculus of rock deformation and geophysical concepts in an easily understandable format.
Weve found out that most kids dont do poorly based on a "fear of the science" but of an "Inability to pick up on the math".

1 Reply

@farmerman,

Quote:

Ive been working with a on-staff professor of physics partner on "simplifying AND ENTERTAINIFYING" THE CONCEPTS OF DIFFERENTIL AND INTEGRAL CALCULUS,

I wish this/your approach to these subjects had been used in all the text books I had in school.
The horrid approach used in most of them has been my pet peeve with education for decades.

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@maxdancona,

Quote:

They are the solutions for Schrödinger's equations in three dimensions.

So, are you saying that is what a hydrogen atomic orbital looks like in three dimensions? Or, just the solutions to the equations look that way, but they don't represent the actual three dimensional shape of the actual atomic orbital in any real way?

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@brianjakub,

Can you please define what you mean by "looks like"? That phrase makes no sense to me.

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@brianjakub,

Let me try to answer your question seriously.

Yes, the Schrodinger equation represents something "real", in that they make predictions that can then be verified by experiment. No, these orbitals don't "look" that way... because to look at something you reflect light off of it into your eyes which doesn't make any sense for many reasons.

The surfaces (shapes) of these orbitals aren't real... they are some arbitrary cutoff point to the value of the wave function. It is a visualization, not an actual shape. And these are values of a wave function that correlate to something that has been simplified as "your chance of finding an electron as a particle at that location".

For you to understand this with any more depth, you need to understand what a matter wave is.

There are a bunch of ways that scientists and writers have tried to simplify things... they will tell you about the wave-particle duality. They will tell you that it is a statistical approximation. All of these things are grossly oversimplified... they are kind of true, but they also are misleading.

If you took a Quantum Mechanics class (which I would recommend if you are really interested in this) you would not only learn to solve the wave functions, you would also discuss the predictions behind these functions and read the papers that have been confirmed by experiment.

The main point I am making is that these diagrams represent something deeper than the shape of orbitals. To understand them, you have to understand the math and the theory that are used to make them.

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@maxdancona,

For anyone who wants a pretty good description of Quantum Mechanics without the mathematical background, I recommend "In Search of Schrodinger's Cat" by John Gribbon.

He goes through the experiments and does a pretty good job explaining the mathematical results (without actually going into the mathematics). And he does a pretty good job of explaining how Quantum Physics is so counter-intuitive.

This is one of the best-written explanations I have seen for laypeople. But even so, you have to trust him about the math, and you really can't get a deep understanding without diving into the math. He does an admirable job, but it doesn't really go very deep into understanding this strange world.

This is why Physics students spend so much time wrestling with the math and theory leading up to this topic.

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@maxdancona,

Thank you for such a concise answer.

Quote:

Yes, the Schrodinger equation represents something "real", in that they make predictions that can then be verified by experiment. No, these orbitals don't "look" that way... because to look at something you reflect light off of it into your eyes which doesn't make any sense for many reasons.

The surfaces (shapes) of these orbitals aren't real... they are some arbitrary cutoff point to the value of the wave function. It is a visualization, not an actual shape. And these are values of a wave function that correlate to something that has been simplified as "your chance of finding an electron as a particle at that location".

For you to understand this with any more depth, you need to understand what a matter wave is.

There are a bunch of ways that scientists and writers have tried to simplify things... they will tell you about the wave-particle duality. They will tell you that it is a statistical approximation. All of these things are grossly oversimplified... they are kind of true, but they also are misleading.

I read the following, understood it.

Quote:

Shape of Orbitals
Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot, however, show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability density | ψ(r, θ, φ) |2 has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour. Although | ψ |2 as the square of an absolute value is everywhere non-negative, the sign of the wave function ψ(r, θ, φ) is often indicated in each subregion of the orbital picture.

and it agrees with what you said except for this:

you say,"The surfaces (shapes) of these orbitals aren't real... they are some arbitrary cutoff point to the value of the wave function. It is a visualization, not an actual shape. And these are values of a wave function that correlate to something that has been simplified as "your chance of finding an electron as a particle at that location".

wiki says,"The diagrams cannot, however, show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability density | ψ(r, θ, φ) |2 has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour."

Wiki doesn't go as far as calling an approximation "not real". I think it is a fact that most atoms are not occupying infinite volumes of space. But some are closer than others. Some are radioactive, or are in a star, or an electron gun. The electrons in those situations can be a lot closer to infinity than the approximate contour surfaces represent. But, since a hydrogen atom does occupy a region that is inside the contour surfaces approximated by the equation in a lot of situations, is it safe to assume that at low energy the orbitals could be represented by that surface? (even if its too small to sense with a detector requiring light waves as the lower limit of size)

Quote:

The main point I am making is that these diagrams represent something deeper than the shape of orbitals. To understand them, you have to understand the math and the theory that are used to make them.

Can most hydrogen atoms' orbitals, under normal circumstances, be represented by these approximated contour surfaces? Could you explain what you mean by deeper? I realize wave particle duality is a very hard to understand idea mathematically. Do you mean that it hard to explain, and impossible to visualize as an image in one's imagination?

Quote:

If you took a Quantum Mechanics class (which I would recommend if you are really interested in this) you would not only learn to solve the wave functions, you would also discuss the predictions behind these functions and read the papers that have been confirmed by experiment.

But, would they help me visualize what the predictions behind these functions represent, and why the contour surfaces representing them when printed on paper look the way they do?

1 Reply

@brianjakub,

I hope you are getting the main point of what I am saying. That language of physics is mathematics. Physicists developing an understanding start with math, and then develop experiments to confirm their mathematical models (occasional they reverse this process, but it always comes down to math). You can't understand Physics without understanding the Math.

When a Physics student starts studying Quantum mechanics she will already have the mathematical background. She will start with Schrodinger's equations and solving them for simple cases (generally the first cases are one-dimensional potential energy wells). The results are startling... the are described as electrons passing through walls... but that doesn't really describe what is happening. Again it is the math that is counterintutive. All through the process the student is asked to understand the experiments that validate that the mathematical results (as strange as they are) are correct.

Actually this is how QM was discovered (obviously a brief summary). The Physicists did the math starting with light. Then this grad student named De Broglie suggested that maybe the same math applied to matter (i.e. electrons). The Physicists did the math, some of them thought it was cool... some of them right away thought the idea was ridiculous. They did out the math and all of them said "gee this is strange". Then they figured out the experiments to do to test this new strange math, and lo and behold, the experiments confirmed that the math correctly described the behavior of matter (particularly electrons).

The point I am laboriously making is this No one, not wikipedia, not I not anyone can adequately explain modern Physics to you without giving you an understand of the math and the experiments used to validate the mathematical models. There are no short cuts. If you don't understand the math... you will inevitably end up with deep misconceptions about what the Physics is really saying.

Now back to the wikipedia article... It does a pretty good job, but it doesn't really explain what is going on. The phrase "where the electrons are likely to be found" is an interesting phrase that I have trouble really explaining. This is a problem because "where you are likely to find an electron" has a lot to do with how you are looking for it. Read about the Heisenburg uncertainty principal if you want to see how problematic this is... or almost as good, read the double slit experiment results in the book I recommend.

Quote:

But, would they help me visualize what the predictions behind these functions represent, and why the contour surfaces representing them when printed on paper look the way they do?

These contour surfaces are solutions in three dimensions to the Schrodinger's equation. The surfaces are drawn at some value (maybe 0.9). That is what they are.

I can't give you more than that. If you take the time to understand the math in Schrodingers equation and the experiments that validate it, then you will have a much better understanding of what these diagrams mean. Sorry, I can't give you more than that.

1 Reply

@maxdancona,

Quote:

And these are values of a wave function that correlate to something that has been simplified as "your chance of finding an electron as a particle at that location".

Related to this, I wonder if you can explain an obvious contradiction for me. It's about the proof that an electron acts as a wave in the famous '2 slot' experiment. There is something left out of the experiment that I may be missing.

It is said that electrons fired at the two slots will cause an interference and cancellation pattern just as light or waves on water do. But that is demonstrably false in practice in the case of the CRT type color picture tube where electrons act predictably as particles. Most use holes in the shadow mask instead of slots but the 'Trinitron' type even used slots so it should be a valid comparison.

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@Leadfoot,

Leadfoot, it is not "demonstrably false". There are mathematical models predicting the interference pattern you see in the double slit experiment. I have done this experiment in my University studies in many forms (including cool studies with crystals). The math accurately makes predictions that are validated by the experiments.

If you do out the math to make a mathematical prediction and then run a valid experiment that contradicts it, then it would be "demonstrably false". But all you have done is made a guess without doing any mathematical calculation and based on your own misunderstanding have declared it to be "demonstrably false".

Show me a mathematical predication and then give me measurements about the size of the slits, the distance between the slits and a mathematical description of what interference you expect to see, then we can talk about whether the Trinitron shows that interference, and whether if it does it would be large enough an effect to be detectable.

I don't know very much about Trinitron. I have done experiments that confirm Schrodinger's equation and I can tell you from experience that the Physics was confirmed by all the experiments I did.

If you could actually prove the theory was "demonstrably false", you would become famous... probably win a Nobel prize. Of course, for you to do this you are going to have to learn the mathematics.

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@Leadfoot,

Here you go Leadfoot. Of course this is just a demonstration, the presenter would still have to show the mathematics to make this a valid proof of anything. But it does work.

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@maxdancona,

Quote:

Here you go Leadfoot. Of course this is just a demonstration, the presenter would still have to show the mathematics to make this a valid proof of anything. But it does work.

Not the same case at all. Firing through graphite is not the same as the slot experiment.

I said it was demonstrably false because color TV CRTs do work. If electrons behaved when going through slots as you say they do, the colors would be all smeary and impure. They aren't.

I'm sure there is an explanation for this discrepancy but you don't know what it is.

1 Reply

@Leadfoot,

There are several possible explanations, one is that given the energy of the beam and the distance between the slots the effect is small enough to not notice. You would have to do the math to know what effect to expect.

Of course I don't understand the technology. It could be there is another piece of the device to change the math. I am sure the engineers who designed the technology understood the physics involved.

Without doing the math though. This is all just empty speculation.

1 Reply

@maxdancona,

Quote:

one is that given the energy of the beam and the distance between the slots the effect is small enough to not notice.

Answer could be related to that. The slots are the width of the target phosphor stripes, 1 slot per group of 3 stripes. The stripes are in the range of .003". Distance of slot to stripes - about .25 - .5" but that's a guess. Gun to slot distance about 13 - 24". The 3 side by side guns are focused and aimed so that they all hit the same spot at the slotted mask. The angular difference of the beams determines which of the 3 stripes a particular gun hits.

Don't expect you to figure out the answer from this crude data but just to give you an idea of the arrangement.

Energy of the beam is high enough that leaded glass is required to shield the viewer from x-rays

1 Reply

@Leadfoot,

.003" inches is 76,000 nm. That is pretty big. The DeBroglie wavelength of an typical electron beam is measured in 1 or 2 nm (if I remember correctly , tt has been a couple of decades). The separation of the slits compared to the wavelength determines the interference pattern. It seems reasonable to me, based on these quick estimates, that the interference for the situation is too small an effect to be noticed.

I am just estimating now (same as you). This conversation is just empty speculation until we do the math. It isn't really worth it to me right now... and you are the one who is trying to disprove modern Physics.

Sony hires people with Ph.d's in physics to work as engineers. They studied the math and were well aware of Schrodinger's equation. I am sure that if they had broken the laws of physics, they would have written a paper about it and collected their fame and fortune and Nobel prizes. Don't you think?

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@maxdancona,

Quote:

and you are the one who is trying to disprove modern Physics.

You & farmer keep saying this but it is not true. I'm trying to understand why the illustrations in text books don't match up with this real world example. Maybe your explanation is right.

But the charge that I'm trying to disprove modern physics is just bullshit. Testing and understanding apparent contradictions is an important aspect of science. I have no doubt that there is a coherent answer that fits with the theory.

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@maxdancona,

Quote:

Now back to the wikipedia article... It does a pretty good job, but it doesn't really explain what is going on. The phrase "where the electrons are likely to be found" is an interesting phrase that I have trouble really explaining. This is a problem because "where you are likely to find an electron" has a lot to do with how you are looking for it. Read about the Heisenburg uncertainty principal if you want to see how problematic this is... or almost as good, read the double slit experiment results in the book I recommend.

Is the math looking for the electrons, or it is predicting with a 90 percent chance of being right in the example given? Because of the uncertainty principle it is very hard to detect the exact location or velocity. ( the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. ) So, even the math has room for error, but the specific locations are represented by a thee dimensional surface. Can anyone hypothesize, or speculate, why the possible locations are represented by these three dimensional surfaces?

Quote:

I can't give you more than that. If you take the time to understand the math in Schrodingers equation and the experiments that validate it, then you will have a much better understanding of what these diagrams mean. Sorry, I can't give you more than that.

Would it be wrong to speculate that the shapes mean that an electron is held inside that surface 90 percent of the time by a boson?

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@Setanta,

Sorry, you are just as bad. You hope that dumping on him elevates you. No, he AND YOU are in the same boat.

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@John316,

It is so obviously untrue that matter entered and will exit from a single point that it is astounding that scientists have even suggested it.

Matter is entering and exiting the hole associated with its own galaxy and this process is happening at varying timescales for each galaxy throughout the universe.

Who cares how much wasted effort they have put into the gravity and single Big Bang theories when they are clearly flawed theories.

I gave up on half logic theories years ago because these theories are utter nonsense.

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@Jasper10,

Science is SYMMETRICAL.

The gravity theory is not a SYMMETRICAL theory.It’s a theory stuck on one side of the fence.

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