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Science Section => Science General Discussion => Physics & Cosmology => Topic started by: Baruch on January 05, 2018, 05:25:40 PM

Title: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on January 05, 2018, 05:25:40 PM
https://www.youtube.com/watch?v=OCuaBmAzqek

Notice that this applies, to a single electron, your universe consists of a single electron in isolation (no measurement).  Not a realistic condition.

So to make it more realistic, we can start with a single electron moving in an EM field (Quantum Electrodynamics).  To apply it further, to the EM field itself we get Relativistic Quantum Field Theory.  One comeuppance is that an election in a EM field, moving relativistically, can't have a single trajectory, because of QM or because of Relativity, but the combination means that it can't even be a single electron, but an infinity of them (many worlds theory).  The problem with quantum gravity, is that the Pythagorean equation ain't exact anymore, but approximate (because of space-time curvature).

The Dirac equation by assumptions, only works in a flat space-time, so without gravity.  But Einstein showed that Special Relativity wasn't consistent, without General Relativity.  This means that the Dirac Equation in some subtle way, isn't self consistent (in all circumstances).  It works plenty well in many circumstances (but has to be solved numerically, not in closed form) ... remember in this first video, that the energy of the election has become an infinite series.

The whole series for the Dirac Equation is in 3 parts.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 02, 2018, 05:48:56 AM
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https://www.youtube.com/watch?v=OCuaBmAzqek

Notice that this applies, to a single electron, your universe consists of a single electron in isolation (no measurement).  Not a realistic condition.

So to make it more realistic, we can start with a single electron moving in an EM field (Quantum Electrodynamics).  To apply it further, to the EM field itself we get Relativistic Quantum Field Theory.  One comeuppance is that an election in a EM field, moving relativistically, can't have a single trajectory, because of QM or because of Relativity, but the combination means that it can't even be a single electron, but an infinity of them (many worlds theory).  The problem with quantum gravity, is that the Pythagorean equation ain't exact anymore, but approximate (because of space-time curvature).

The Dirac equation by assumptions, only works in a flat space-time, so without gravity.  But Einstein showed that Special Relativity wasn't consistent, without General Relativity.  This means that the Dirac Equation in some subtle way, isn't self consistent (in all circumstances).  It works plenty well in many circumstances (but has to be solved numerically, not in closed form) ... remember in this first video, that the energy of the election has become an infinite series.

The whole series for the Dirac Equation is in 3 parts.

Gravity matters.  And as you yourself say, the Dirac Equation isn't self-consistent.  And electrons aren't infinite.  Things that don't make sense don't make sense.

I recall when I was taking Astronomy 101 in 1968, I told the Professor that I didn't see how galactic spiral arms could exist as the galaxy revolved.  He dismissed me, saying that they moved so slowly that there hadn't been time for them to collapse the arms. 

Guess who was wrong?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 02, 2018, 12:53:39 PM
Galaxy arms are more of a wave thing, not a arm thing.  There are physical impacts moving out from the galactic core all the time (giant black hole).  Next one gets to us, we are toast.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 02, 2018, 01:01:42 PM
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Galaxy arms are more of a wave thing, not a arm thing.  There are physical impacts moving out from the galactic core all the time (giant black hole).  Next one gets to us, we are toast.

Um "no".  Last I read, spiral galaxy arms are held in place by dark matter, which completely overwhelmes all normal matter gravitationally.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 02, 2018, 01:05:13 PM
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Um "no".  Last I read, spiral galaxy arms are held in place by dark matter, which completely overwhelmes all normal matter gravitationally.

Speculation.  You have dark matter between the ears ;-)
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Unbeliever on February 02, 2018, 01:13:12 PM
There's also Wheeler's idea that the universe really only has one electron:


https://www.youtube.com/watch?v=9dqtW9MslFk
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 02, 2018, 01:34:19 PM
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There's also Wheeler's idea that the universe really only has one electron:


https://www.youtube.com/watch?v=9dqtW9MslFk

That one is too much for me.  Apparently, I have a dark matter banana in my ear...
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Unbeliever on February 02, 2018, 01:37:21 PM
Is that a dark matter banana in your ear, or are you glad to see me?

:)
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 02, 2018, 01:38:34 PM
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Is that a dark matter banana in your ear, or are you glad to see me?

:)

Hey?  What?   Sorry, I have a dark banana meteorite in my ear.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 02, 2018, 07:07:10 PM
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There's also Wheeler's idea that the universe really only has one electron:


https://www.youtube.com/watch?v=9dqtW9MslFk

That comes from Feynman diagrams.  It easily explains why all electrons are alike ;-)

It would only work, if there was almost exactly the same amount of anti-matter as matter ... and we don't see that.  Dr Alfven ... a plasma physicist, tried to get around this, by saying that there must be much anti-matter out there, even anti-galaxies.  The unsymmetrical decay of K-mesons discovered in the 1960s, pretty much explains why there is so little anti-matter ... basically there could have been equal amounts early in the Big Bang, but by the time hydrogen became neutral, the asymmetry had made sure that almost all of it had decayed into ordinary matter.

https://en.wikipedia.org/wiki/Kaon
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 07, 2018, 06:26:59 AM
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That comes from Feynman diagrams.  It easily explains why all electrons are alike ;-)

It would only work, if there was almost exactly the same amount of anti-matter as matter ... and we don't see that.  Dr Alfven ... a plasma physicist, tried to get around this, by saying that there must be much anti-matter out there, even anti-galaxies.  The unsymmetrical decay of K-mesons discovered in the 1960s, pretty much explains why there is so little anti-matter ... basically there could have been equal amounts early in the Big Bang, but by the time hydrogen became neutral, the asymmetry had made sure that almost all of it had decayed into ordinary matter.

https://en.wikipedia.org/wiki/Kaon

I thought the idea was that there were (for random causes) like a billion (to the whatever) matter atoms and a billion (to the whatever) minus one anti-matter atoms and what was left was matter.  Of course, had it been the other way around, we would still consider that "matter". 

But that was before dark matter and dark energy...
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 07, 2018, 01:39:44 PM
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I thought the idea was that there were (for random causes) like a billion (to the whatever) matter atoms and a billion (to the whatever) minus one anti-matter atoms and what was left was matter.  Of course, had it been the other way around, we would still consider that "matter". 

But that was before dark matter and dark energy...
This is exactly right. The one-electron/proton/neutron theory would require there to be almost exactly as much antimatter in the universe as there is matter. However, we don't seem to find it in sufficient quantity to make the theory viable. Even if we called matter antimatter and vice versa, it doesn't matter — in order for the theory to fly, you need to have them in about equal in quantity, which we don't find anywhere.

Though how Baruch thinks that the Dirac Sea implies infinite worlds is beyond me, because it doesn't.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 07, 2018, 08:54:48 PM
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This is exactly right. The one-electron/proton/neutron theory would require there to be almost exactly as much antimatter in the universe as there is matter. However, we don't seem to find it in sufficient quantity to make the theory viable. Even if we called matter antimatter and vice versa, it doesn't matter — in order for the theory to fly, you need to have them in about equal in quantity, which we don't find anywhere.

Though how Baruch thinks that the Dirac Sea implies infinite worlds is beyond me, because it doesn't.

Infinite worlds, comes from the multiverse interpretation of QFT ... which was derived from the Dirac equation.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 07, 2018, 11:23:38 PM
Baruch, the many worlds interpretation of quantum mechanics is not a special implication of the Dirac equation. Any quantum theory that includes superposition that can decohere on observation implies the many worlds interpretation as much as the Copenhagen interpretation. They are both, after all, interpretations of what happens to the quantum system and the universe as the weirdness of the quantum world yields to the classical determinism of the macroworld. Many worlds is not dependent upon nor is implied by QFTs, let alone the Dirac equation specifically.

The other thing is that the concept of a quantum field predated the Dirac equation; the Klein–Gordon equation (https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation) predated the Dirac equation by two years, and Wolfgang Pauli came up with a similar idea (https://en.wikipedia.org/wiki/Pauli_equation) around the same time.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 07, 2018, 11:35:38 PM
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Baruch, the many worlds interpretation of quantum mechanics is not a special implication of the Dirac equation. Any quantum theory that includes superposition that can decohere on observation implies the many worlds interpretation as much as the Copenhagen interpretation. They are both, after all, interpretations of what happens to the quantum system and the universe as the weirdness of the quantum world yields to the classical determinism of the macroworld. Many worlds is not dependent upon nor is implied by QFTs, let alone the Dirac equation specifically.

The other thing is that the concept of a quantum field predated the Dirac equation; the Klein–Gordon equation (https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation) predated the Dirac equation by two years, and Wolfgang Pauli came up with a similar idea (https://en.wikipedia.org/wiki/Pauli_equation) around the same time.

Thanks for adding more detail, but it didn't actually matter.  You simply like to ... add on.  I do too.  Let me know when you get your Nobel Prize or Field Medal, won't you?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 08, 2018, 09:01:27 AM
Baruch, look carefully. It's not a mere "add-on"; it is a correction. The Dirac equation didn't imply many worlds any more than the Schrodinger equation did. Many worlds is a completely independent proposition from the equations used to describe particle behavior.

Why are you so against being corrected, huh?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 08, 2018, 12:51:22 PM
Why do you like to split hairs?  Got Rogaine?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 08, 2018, 02:04:42 PM
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Why do you like to split hairs?
Because "splitting hairs" is our stock in trade. Splitting hairs in our measurements is how we came up with quantum mechanics in the first place. QFT came from caring about the nitty-gritty details of the implications of relativity coupled with quantum principles. It's because what looks like splitting hairs to the ordinary person is actually splitting logs to us.

Quantum mechanics is hard enough to understand without the misconceptions. I would thank you not to be spreading them around. I would also thank you to care about the accuracy of what you would teach others.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 08, 2018, 07:17:31 PM
I am sure you are a god of your own universe ... I am only a demigod in this one ;-)
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 08, 2018, 07:41:01 PM
Yeah, we had other people believe that they're Jesus Christ, too. Didn't turn out so well.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 08, 2018, 08:12:44 PM
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Yeah, we had other people believe that they're Jesus Christ, too. Didn't turn out so well.

Nope, Jewish yes, Jesus no.  And you are neither.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 08, 2018, 11:54:57 PM
I am completely fine with not being a Jesus. The only one who claimed to be a demigod was you, which is a fair description of Jesus Christ.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 09, 2018, 01:57:33 AM
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Thanks for adding more detail, but it didn't actually matter.  You simply like to ... add on.  I do too.  Let me know when you get your Nobel Prize or Field Medal, won't you?

I notice you didn't exactly answer her questions...
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 09, 2018, 07:11:18 AM
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I notice you didn't exactly answer her questions...

Hakurei and I have a history.  You and I have a different history.  Being photographically minded (sometimes) means that any new conversation is a continuation of an older one.  That can be confusing to the two, depending on who is forgetful.  For a person outside that context ... it can't be easy.

Direct answers are sometimes rude.  I try to self-moderate my rudeness.  Having chutzpa isn't the same as being an asshole (referring to myself).  Ellipsis is how I sometimes manifest that self-moderation.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 09, 2018, 07:12:01 AM
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I am completely fine with not being a Jesus. The only one who claimed to be a demigod was you, which is a fair description of Jesus Christ.

That is more true than you realize.  But everyone is on their own path, beating their own drum, or something else ...
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 09, 2018, 08:53:03 PM
Photographic (sometimes) memory, eh? Well, in many ways forgiving is forgetting, so that does shed some light on our history. I always try to treat each new thread as if it were a fresh start, because life's too short to carry grudges.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 09, 2018, 11:55:14 PM
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Photographic (sometimes) memory, eh? Well, in many ways forgiving is forgetting, so that does shed some light on our history. I always try to treat each new thread as if it were a fresh start, because life's too short to carry grudges.

I am more of an elephant, and you stay true to character.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Hakurei Reimu on February 10, 2018, 07:31:55 PM
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I am more of an elephant, and you stay true to character.
Oh? What's that?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Unbeliever on February 11, 2018, 06:05:07 PM
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life's too short to carry grudges.
We don't need no stinking grudges!



(https://gloriagrehl.files.wordpress.com/2014/11/11-5-14-badges.png)
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 11, 2018, 07:43:19 PM
And don't mine gold ore on Mexican territory, Gringos!
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 13, 2018, 03:16:02 AM
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Hakurei and I have a history.  You and I have a different history.  Being photographically minded (sometimes) means that any new conversation is a continuation of an older one.  That can be confusing to the two, depending on who is forgetful.  For a person outside that context ... it can't be easy.

Direct answers are sometimes rude.  I try to self-moderate my rudeness.  Having chutzpa isn't the same as being an asshole (referring to myself).  Ellipsis is how I sometimes manifest that self-moderation.

You remember past posts that well without looking them up?  I'm impressed.  The question may be whether you image you do or actually do.  Can you know the difference?
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Baruch on February 13, 2018, 05:43:44 AM
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You remember past posts that well without looking them up?  I'm impressed.  The question may be whether you image you do or actually do.  Can you know the difference?

More like, I get an impression of a persons character, so I know what to expect.  Perfectly normal, not special.  I have some photographic memory, but that isn't what I was talking about.
Title: Re: Here is the actual math for the Dirac equation (relativistic quantum electron)
Post by: Cavebear on February 15, 2018, 03:36:51 AM
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More like, I get an impression of a persons character, so I know what to expect.  Perfectly normal, not special.  I have some photographic memory, but that isn't what I was talking about.

We all learn an impression of others' character.  That isn't very special.