An Alternative Equation for the Wavefunction and its Eigenfunctions

[John Henke]

Do physicists know what scale time is on relative to length?

Edited May 7, 2020 by John Henke

[Kartazion]

2 minutes ago, John Henke said:

Do physicists know what scale time is on relative to length?

Planck ?

[John Henke]

That does suggest it is 1 to 1 and that is probably the case. I probably need to rework thw theory. I think the mathematical phenomena is still promising even if Ive messed it up somewhere.

[Mordred]

Use the interval length as per GR.

[math](ct,x,y,z)[/math]

Why do you have e^2=p^2+m^2 ?

That isn't the formula I gave you for energy momentum you need the full formula

[John Henke]

Thats the equation in natural units.

[Mordred]

No the equation I gave is not natural units.

The equation you have would give incorrect values. Try it and use the same mass and velocity for each equation.

Edited May 7, 2020 by Mordred

[swansont]

On 5/4/2020 at 4:09 PM, John Henke said:

The goal of this post is to make clear how to run these calculations and the logic behind them has been omitted except where it is needed to illustrate how to run the calculations. I’ve removed delta, epsilon, iota, rho, kappa and lowercase alpha as well as any other point of confusion I could find. This has made the post long, but the math should now be well defined.

 

Saying e.g. omega is similar to the physics definition but is still present when there is no spin isn't particularly helpful.

 

 

On 5/4/2020 at 4:09 PM, John Henke said:

 

Why are omega bar and k bar equal to one? What physical significance does this have?

How does this compare to a solution from Schrödinger's equation? What boundary conditions did you apply?

Why is this graphed vs time? Can you give the solution for the wave function as a function of position?

 

 

 

[John Henke]

7 hours ago, swansont said:

Saying e.g. omega is similar to the physics definition but is still present when there is no spin isn't particularly helpful.

I say that because one of the more speculative parts of my theory is that it says that a particle is the same as their QM partners except they may have no spin and may have no angular momentum but they still have k bar and omega bar values, so it wouldn't make sense to say they had, for example, an angular frequency, but they still have energy based on omega overbar.

7 hours ago, swansont said:

Why are omega bar and k bar equal to one? What physical significance does this have?

They're variables, and I just chose them arbitrarily. I'm in the process of redefining them so that they work correctly, so I won't go into too much detail now.

7 hours ago, swansont said:

How does this compare to a solution from Schrödinger's equation? What boundary conditions did you apply?

It's more or less the same. Here's an example of a particle in a square well. I will first give the x eigenvalue form. This is important because this equation occurs within the equation for the waveform and the area over which the waveform spans is determined by the area over which its x eigenfunction spans. Note that both eigenfunctions span a distance of 2 meaning that both waveforms are in an infinite square well with walls a distance apart of 2.

X Eigenfunction with k bar=1

Waveform in Infinite Square well with k=1

X Eigenfunction with k bar=2.

Waveform in Infinite Square well with k=2.

And the same pattern would hold for higher integer values of k.

7 hours ago, swansont said:

Why is this graphed vs time? Can you give the solution for the wave function as a function of position?

There may be a way to graph it as a function of position. I will look into that. But this represents one of the biggest differences between my waveform and QM's wavefunction. QM has the position as an input and mine has the position as an output (which is intuitive enough as it's essentially a naturally occurring x eigenfunction). This is why I had to include the x eigenfunction in the above example, to show that the waveforms with k=1 and k=2 both spanned the same well because even though the k=2 exists over more initial time, its x eigenvalues still only span a distance of 2, same as for k=1.

At any rate, I'm in the process of rewriting my theory and time is one of the things I will redefine in my post tomorrow.

Infinite Square Well k1 and k2.nb

Edited May 8, 2020 by John Henke

[Mordred]

One of the most important details you are consistently missing.

 How does your wavefunctions and symbology work with mainstream physics ?

If I cannot apply standard formulas of QM/QFT to what you have. Then there is a problem I. Houston.

 A good workable theory would mean I could take any related formula beyond what you have applied and find accuracy.

 Thus far...

Take your wavefunction graphs as one example. 

Where is the highest probability of a particle ? You have graphs that have a consistent rate of increase in amplitude from one waveform period to the next. Yet claim this is a probability function.

Good luck on that

 

Edited May 8, 2020 by Mordred

[John Henke]

17 hours ago, Mordred said:

How does your wavefunctions and symbology work with mainstream physics ?

That's one of the things I'm working on right now, and I'm so far happy with my progress.

17 hours ago, Mordred said:

Good luck on that

Thank you. And thank you for your input. It's helped a lot.

Edited May 9, 2020 by John Henke

[Mordred]

On 5/2/2020 at 12:47 PM, swansont said:

You might also find a simple QM problem and work through the solution to it.

Then this is probably the best advise given this thread.

I highly recommend it. This will give you an informed practical understanding of when and where different QM wavefunctions answer specific questions as well as the mathematics used to interpret those wavefunctions.

One question often in an exam is 

"Draw a wavefunction (with given criteria example an electron in such and such orbital) at T=0. ?

That question should highlight one of Swansonts relevant questions.

(A very common mistake is taking classical understandings of waveforms and wavefunctions and believing they are treated the same in QM. While their are similarities there are are distinctive differences) 

Examples discrete energy levels, probability functions and weighted density of probability functions under graph.

Another example of a typical wavefunction question. Given the wavefunction and the following potential well. With the infinite potential at such and such location.

Give the probability of the particle (always has some details) escaping the potential well.

(Quantum tunneling question)

I also hope you that when the above advise you would recognize the need to be able to describe waveforms in different detector orientations ie spin in the Stern Gerlach detector. 

 

 

Edited May 9, 2020 by Mordred

[John Henke]

50 minutes ago, Mordred said:

On 5/3/2020 at 3:47 AM, swansont said:

You might also find a simple QM problem and work through the solution to it.

Then this is probably the best advise given this thread.

Well, I thought I was, but I will try to make my terms equate to the terms in Griffith's.

50 minutes ago, Mordred said:

I also hope you that when the above advise you would recognize the need to be able to describe waveforms in different detector orientations ie spin in the Stern Gerlach detector. 

I'm on it. I'll post something relatively soon.

Edited May 9, 2020 by John Henke

[Mordred]

Griffiths books are excellent I have a copy of his Introductory to Quantum mechanics. 2nd edition. If I recall he also has a good example of even odd parity wavefunctions.

(You may note you will want to change your symbology to avoid conflict with standardized symbols in QM) 

That will make it far easier for readers familiar with QM to avoid added confusion.

+1 for dedicating yourself to learning the mainstream to properly test your own theory. 

 

Edited May 9, 2020 by Mordred

[studiot]

2 hours ago, Mordred said:

+1 for dedicating yourself to learning the mainstream to properly test your own theory. 

Agreed +1 again.

But please remember that not everyone is a fan of Griffiths. I only know his Electrodynamics and find it not sufficiently to my taste to want to look at other books by him.
So be aware there are already several approaches and unfortunately notations to QM.

I don't understand why you seem so doggedly determined not to discuss differential equations?

[Mordred]

32 minutes ago, studiot said:

 

I don't understand why you seem so doggedly determined not to discuss differential equations?

Lol I predict that will be an absolute need 

[John Henke]

20 hours ago, studiot said:

I don't understand why you seem so doggedly determined not to discuss differential equations?

I just haven't worked on it much yet. I will put that toward the top of my list of things to do. There's a lot to do and it all takes time.

Edited May 10, 2020 by John Henke

[swansont]

On 5/8/2020 at 2:15 PM, John Henke said:

I say that because one of the more speculative parts of my theory is that it says that a particle is the same as their QM partners except they may have no spin and may have no angular momentum but they still have k bar and omega bar values, so it wouldn't make sense to say they had, for example, an angular frequency, but they still have energy based on omega overbar.

You're saying they are the same, only different. So that's as clear as mud.

What particle would have no angular momentum but have energy based on this variable?

On 5/8/2020 at 2:15 PM, John Henke said:

They're variables, and I just chose them arbitrarily. I'm in the process of redefining them so that they work correctly, so I won't go into too much detail now.

Arbitrarily? Is this a joke?

Nature isn't arbitrary. These variables have to be based on something. You can't just make it up. If you did, you can pick any answer you want out of the results. That's not how this works. An eigenstate has one result.

 

On 5/8/2020 at 2:15 PM, John Henke said:

It's more or less the same. Here's an example of a particle in a square well. I will first give the x eigenvalue form. This is important because this equation occurs within the equation for the waveform and the area over which the waveform spans is determined by the area over which its x eigenfunction spans. Note that both eigenfunctions span a distance of 2 meaning that both waveforms are in an infinite square well with walls a distance apart of 2.

X Eigenfunction with k bar=1

 

For what value of x does this hold? Why are there two curves? What is the significance of t being negative?

 

On 5/8/2020 at 2:15 PM, John Henke said:

There may be a way to graph it as a function of position. I will look into that. But this represents one of the biggest differences between my waveform and QM's wavefunction. QM has the position as an input and mine has the position as an output (which is intuitive enough as it's essentially a naturally occurring x eigenfunction).

But you don't have position as an output. Your graphs are plotted as a function of t. How does one get position information?

 

On 5/8/2020 at 2:15 PM, John Henke said:

This is why I had to include the x eigenfunction in the above example, to show that the waveforms with k=1 and k=2 both spanned the same well because even though the k=2 exists over more initial time, its x eigenvalues still only span a distance of 2, same as for k=1.

More initial time? What does that mean?

 

[studiot]

45 minutes ago, swansont said:

Arbitrarily? Is this a joke?

Nature isn't arbitrary. These variables have to be based on something. You can't just make it up. If you did, you can pick any answer you want out of the results. That's not how this works. An eigenstate has one result.

Just a guess but I have been wondering if John's method of analysis is a form of curve fitting given the range of possible solutions to the wave equation and his reluctance to discuss the mathematics of it.

[John Henke]

6 hours ago, studiot said:

Just a guess but I have been wondering if John's method of analysis is a form of curve fitting given the range of possible solutions to the wave equation and his reluctance to discuss the mathematics of it.

This is going to be long, but that statement makes it so painfully clear that this theory has not yet been well understood.

I would argue that the only philosophically feasible option for a universe being created from nothing is one where 0=U where U is the universe. If that’s true, then the universe is purely mathematical in structure and the sum of its positive and negative parts equates to zero. I would hold that it’s impossible to explain a viable alternative to this without resorting to something abstract and/or mystical. If you have one, then you can prove me wrong.

Otherwise let’s assume the universe is purely mathematical in structure, and if it were to be based on the current mathematics, it would have to know what a derivative is and how to take it and then decide to multiply it by -i(hbar). It would have to somehow decide to multiply each position along the x axis by x for the x eigenfunction, etc, etc. To my eye, this is the model that is clearly man-made and has been bent and curved by human will to describe physical phenomena. I’m not questioning that it describes physical phenomena, but I am questioning whether it can itself be physical phenomena in a mathematically structured universe.  Contrast the current model to the relative philosophical simplicity of my model as it transitions from a waveform into an eigenfunction and then even from a quantum wave form to a particle form only ever using the multiplication and division of two different equations—equations that in their original form occupied no more than a quarter of a page each.

And if it’s true that the universe is purely mathematical in structure, then the math must involve waveforms. There are a highly limited number of ways of creating waveforms mathematically, and possibly none that haven’t been discovered, and so the options are limited. I’ve shown a new one, and argued why it could give a natural explanation for the source of the universe. Theoretical physicists have shown another, but has anyone ever argued that it was natural and equated to the mathematical structure of the universe? I know of no philosophy that requires or implicates the current fundamentals of quantum mechanics, and I’m only trying to replace those fundamentals.

So before “guessing” that I’m bending the numbers to my own will, contrast mine to the current model. I have defined certain variables, and to a great degree my mathematics have been bent by me in an attempt to describe physical phenomena. And these are admittedly going to be the points most vulnerable to revision. However, there’s absolutely nothing that’s mystical or poorly defined about my math. And you may disagree, but Mathematica doesn’t.  

A mathematical phenomena that the universe could have used to create itself without consciousness and without choice—that’s what I believe I’ve found though I’m still searching for the specifics.

Tomorrow I will write a post going over my new model of relativity, but also explaining the fundamentals more clearly, addressing all of the recent questions.

Edited May 11, 2020 by John Henke

[Mordred]

I can essentially guarantee the proposal in your last post isn't viable.

 The first thing you must recognize is that energy is simply the ability to perform work. It doesn't exist on its own. So negative energy isn't really applicable. 

 Secondly as I stated before mathematics do not cause anything.

They represent or describe. They cannot cause.

I would recommend a new thread in Speculation with regard to your universe model if you wish to continue pursuing it.

 

Edited May 11, 2020 by Mordred

[John Henke]

58 minutes ago, Mordred said:

I can essentially guarantee the proposal in your last post isn't viable.

 The first thing you must recognize is that energy is simply the ability to perform work. It doesn't exist on its own.

My new model of relativity pretty massively revises the theory. Before you critique it, you should see it.

58 minutes ago, Mordred said:

Secondly as I stated before mathematics do not cause anything.

They represent or describe. They cannot cause.

When I was a kid, I went to a magic show in Las Vegas with my family. The magician disappeared and then reappeared instantly a distance away. It seemed to be clearly the same person. Afterward my family was talking about how it happened and I suggested he had a twin. This was a perfectly reasonable and viable option, but they laughed it off and seemed to think that there must be some more complicated perhaps even more mystical answer. You assume the universe is physical, but I've provided what seems to be a completely feasible explanation to a very difficult question. Can you provide a better alternative?

58 minutes ago, Mordred said:

I would recommend a new thread in Speculation with regard to your universe model if you wish to continue pursuing it.

I wouldn't object to that. Should I just post a new thread?

Has anyone ever proposed an equivalent of 0=U where U is the universe and theres a mostly negative half to the universe that cancels with our mostly positive half? 

Edited May 11, 2020 by John Henke

[Strange]

1 hour ago, John Henke said:

Has anyone ever proposed an equivalent of 0=U where U is the universe and theres a mostly negative half to the universe that cancels with our mostly positive half? 

https://en.wikipedia.org/wiki/Zero-energy_universe

1 hour ago, John Henke said:

would argue that the only philosophically feasible option for a universe being created from nothing is one where 0=U where U is the universe.

There is no evidence the universe was created from nothing.

1 hour ago, John Henke said:

If that’s true, then the universe is purely mathematical in structure

That is a non sequitur.

1 hour ago, John Henke said:

My new model of relativity pretty massively revises the theory.

So it massively revises it but produces the same results?

[John Henke]

7 minutes ago, Strange said:

https://en.wikipedia.org/wiki/Zero-energy_universe

This is energy not math.

7 minutes ago, Strange said:

There is no evidence the universe was created from nothing.

And your alternative explanation for how we got here?

8 minutes ago, Strange said:

That is a non sequitur.

Yes, it is.

8 minutes ago, Strange said:

1 hour ago, John Henke said:

My new model of relativity pretty massively revises the theory.

So it massively revises it but produces the same results?

How is it that two people have already critiqued a model I haven't even released yet? No, it doesn't produce the same results.

[Strange]

20 minutes ago, John Henke said:

This is energy not math.

We know that energy is a component of the universe. One could go so far as to say that the universe is "made of energy".

But, despite Pythagoras's belief, there is no science behind the claim that the "universe is made of math".

21 minutes ago, John Henke said:

And your alternative explanation for how we got here?

There are lots. And even the theories that posits a universe from "nothing" don't start from absolutely nothing. They start from quantum fields, with non-zero energy, etc.

22 minutes ago, John Henke said:

How is it that two people have already critiqued a model I haven't even released yet? No, it doesn't produce the same results.

It wasn't a critique, just a question.

But if it doesn't produce the same results then it doesn't match reality and so it must be wrong.

[John Henke]

41 minutes ago, Strange said:

One could go so far as to say that the universe is "made of energy".

But, despite Pythagoras's belief, there is no science behind the claim that the "universe is made of math".

Made of energy is an abstraction. There is also no science behind saying that the universe has any physicality that transcends a mathematical structure--or, if there is, I'd like to see it.

41 minutes ago, Strange said:

There are lots. And even the theories that posits a universe from "nothing" don't start from absolutely nothing. They start from quantum fields, with non-zero energy, etc.

If you gave me a specific example, I'm willing to bet there would be a lot of assumptions and abstractions used. My explanation requires as few assumptions and abstractions as math itself. You seem to assume that I mean that the universe had a central location of zero, but I don't even assume that. I assume that 0=U and that the universe is mathematical in structure, and that's it--a bare minimum of assumptions and choice and abstraction, this minimum being the key to explaining how the universe could be created without consciousness.

41 minutes ago, Strange said:

But if it doesn't produce the same results then it doesn't match reality and so it must be wrong.

Well, if you're first comment wasn't a critique, this definitely is. I'm not sure I understand the logic of it, but I think you're saying that you think in my mind the equation is the universe and so changing it would make me wrong. That's a straw man. Of course I don't believe that. When I say phenomena, I'm talking about the most basic aspects of my theory, for example the way I get my x eigenfunction. That's as much a mathematical phenomena as Euler's identity. Now theoretical physicists have used Euler's identity and added a bunch of terms to it like k and omega, etc and so too have I explored how the universe might have used this phenomena to create itself. But if the universe did create itself using these equations, I would never dream that my first model would perfectly match up with it. There are a lot of ways of defining things, moving things around, etc as you'll see in my new model tomorrow.

Edited May 11, 2020 by John Henke