# Thread: four-position product needs to be changed

1. ## four-position product needs to be changed

Hi guys,
I took me some time but I finally found some fresh idea what we could do to link field phenomena with space-time definition.

I wait for reviewer comments for the article, but - as always - I would be glad to discuss my idea with you.

First part of my article below
__________________________________________

To simplyfy calculations we assume c=1.

In Special Relativity four-position gives proper-time as product of
(1)

Taking proper-time derivative on above one gets
(2)

One may easy show, that present four-position product definition excludes any filed existence, no matter how we define field!

From (1) one may easy derive
(3)

thus one may easy transform (2) to
(4)

From above using easy calculations one may get
(5)

where is perpendicular component of velocity.

Therefore for radial move () we get

(6)

Substituting above to (2) one gets
(7)

One may easy calculate taking proper-time derivative on above, that for such , time component of four-acceleration vanishes
(8)

Since time component of four-acceleration vanishes only if there is lack of acceleration (resultant acceleration vanishes) so we have just proved that present four-position product definition excludes any acceleration for radial move.

But it is known, that e.g. for radial move of charged particles acceleration exists... And the same time, no matter how we define field, present four-position product definition excludes acceleration for radial move.

It is crucial to understand, that even if one artificially adds a field to Lagrangian, present four-position product definition excludes radial acceleration by definition.

So we need to change somehow four-position product in Special Relativity to ensure possibility of the field presence.

In the next post I propose some solution.
Last edited by pogono; 2019-May-25 at 07:44 PM.

2. Let us then redefine four-position product following way

(9)

where S is normalized (divided by mc) action (Hamiltonian principal function).

We may now assume, that is just specific case where there is no field and no field-related acceleration in the space-time. Let us also assume that in general

(10)

where represents presence of the field and produces generalized field four-vector

(11)

Taking four-gradient on (9) one gets

(12)

where is normalized, generalized four-momentum.

One should ask, how we can ensure for such four-position product, that metric equation remains correct. Let us propose

(13)

what may be treated as part of extended SR definition and ensures that generalized momentum works the way we expect.

One may easy show, that such generalized four-momentum fulfills condition

(14)

where L is normalized Lagrangian (Lagrangian divided by mc). So if we take proper-time derivative on (12) we get

(15)

where is four-acceleration and we use property giving that

(15a)

Let us introduce electromagnetic field four-potential defined as

(16)

All we need now to link electromagnetism with space-time definition is to request that

(17) where q is for charge

It also simplifies a lot field unification with General Relativity theory. We may generalize above reasoning to covariant derivatives and curvilinear coordinates and expect that four-position product will be just Einstein-Hilbert action.

How do you like it?

P.S.
Whole article preprint you may find on my researchgate profile
Last edited by pogono; 2019-May-25 at 08:19 PM.

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Originally Posted by pogono
Hi guys,
I took me some time but I finally found some fresh idea what we could do to link field phenomena with space-time definition.

I wait for reviewer comments for the article, but - as always - I would be glad to discuss my idea with you.

First part of my article below
__________________________________________

To simplyfy calculations we assume c=1.

In Special Relativity four-position gives proper-time as product of
(1)

Taking proper-time derivative on above one gets
(2)

One may easy show, that present four-position product definition excludes any filed existence, no matter how we define field!

From (1) one may easy derive
(3)

thus one may easy transform (2) to
(4)
Basic algebra shows that (4) is incompatible with (3).
So, I cannot take the remainder of handwaving seriously.

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Originally Posted by pogono
Hi guys,

From above using easy calculations one may get
(5)

.
The units on the LHS do not match the ones on the RHS. This makes your numerology hard to take seriously.

5. Originally Posted by giorgio
The units on the LHS do not match the ones on the RHS. This makes your numerology hard to take seriously.
Hi giorgio.
Thanks for the first question.

Calling math "numerology" is a bit rude and ancient Greeks, who invented most of basic math, could feel offended.
But I understand that not everyone has to be familiar with such ancient inventions, so let me help you to go through these equations.

From (2) you get:

(E1)

You divide both sides by

to get

(E2)

Raising above to the square you get

(E3)

One knows form Special Relativity four-position product definition - in oryginal equation (1) - that

(E4)

what yields:

(E5)

(if it is not clear why, I may explain in separated post)

One knows from basics of Special Relativity that
Since we assumed that c=1 (to simplify calculations) we may note this as just

(E6)

So, substituting (E5) and (E6) to equation (E3) we get oryginal equation (4)

(4)

If you calculate above you get

(E7)

One may rewrite above as

(E8)

Now, one may multiply above by to get

(E9)

-----------
Now comes the hardest part because we have to use concept of vectors and its properties.

One may rewrite (E9) as

(E10)

(if this is unclear - let me know and I will explain in separated post)

Next, one knows from basic vector calculus rules, that:

(E11)

where:

u - velocity
- radial component of velocity
- perpendicular component of velocity

(if this is unclear - let me know and I will explain in separated post)

One also knows from basic vector calculus, that:

(E12)

(if this is unclear - let me know and I will explain in separated post)

Joining knowledge from (E11) and (E12) one gets

(E13)

(if this is unclear - let me know and I will explain in separated post)

Therefore using (E13) one may rewrite equation (E10) as oryginal equation (5)

(5)

I hope it helps.

In case of problems with other equations I may recommend some good math textbooks for elementary schools.
You may find inside explanation for concepts of vectors, fractions and quadratic equations we use here.
Last edited by pogono; 2019-May-27 at 03:20 AM. Reason: gramma

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Originally Posted by pogono
Hi giorgio.
Thanks for the first question.

Calling math "numerology" is a bit rude and ancient Greeks, who invented most of basic math, could feel offended.
But I understand that not everyone has to be familiar with such ancient inventions, so let me help you to go through these equations.

From (2) you get:

(E1)
You are mixing something that has dimension of time with something that has dimension of distance multiplied by speed. Your "stuff" is getting worse and worse. No point in looking at the rest, this mistakes are piling up.

7. Originally Posted by giorgio
You are mixing something that has dimension of time with something that has dimension of distance multiplied by speed. Your "stuff" is getting worse and worse. No point in looking at the rest, this mistakes are piling up.
Hi,
i suppose you missed assumption from the begining saying that to simplify calculations we assume that light speed c=1.

This assumption makes dimensions work fine in all above equations.

In case you are not familar with the role of constant "c" in equations:
- it says what is the proportion beetween distance and time dimension (we assume that it is 1 to make calculations easier)
- there is about million physical articles with assumption c=1 made to simplify calculations

In case you are not familiar with the role of any constanst in equation:
- you may recalculate all above equations using "c" in equations
- you may be surprised, bu it still work same fine

Dear mods,
I am here to explain my theory - not basic math or elementary school textbooks issues in physics.
Please, check if giorgio is not socket puppet of some known troll.

8. Originally Posted by pogono
Dear mods,
I am here to explain my theory - not basic math or elementary school textbooks issues in physics.
Please, check if giorgio is not socket puppet of some known troll.
If you have a concern, use the report button, lower left.

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Originally Posted by pogono

To simplyfy calculations we assume c=1.

In Special Relativity four-position gives proper-time as product of
(1)

From (1) one may easy derive
(3)
Here is another error, right off the bat. Contrary to your claim, (3) is obviously false. To help you, doesn't even make sense, physically. What does make sense is . Your paper is littered with this type of mistake.
Last edited by giorgio; 2019-May-27 at 02:06 PM.

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Originally Posted by pogono

Substituting above to (2) one gets
(7)

One may easy calculate taking proper-time derivative on above, that for such , time component of four-acceleration vanishes
(8)

Since time component of four-acceleration vanishes only if there is lack of acceleration (resultant acceleration vanishes) so we have just proved that present four-position product definition excludes any acceleration for radial move.
You get the above erroneous result because you do not understand what represents (see my posts above[/tex].

Q1: pogono, what does represent?

But it is known, that e.g. for radial move of charged particles acceleration exists... And the same time, no matter how we define field, present four-position product definition excludes acceleration for radial move.
You arrive to this incorrect conclusion because of your basic misunderstandings.

So we need to change somehow four-position product in Special Relativity to ensure possibility of the field presence.
"We" do not need to change anything. You, need to figure out your mistakes.

11. Originally Posted by giorgio
Here is another error, right off the bat. Contrary to your claim, (3) is obviously false. To help you, doesn't even make sense, physically. What does make sense is . Your paper is littered with this type of mistake.
Dear macaw,
it makes sense. It is just fraction.
In math you may make fractions with any numbers except 0 in denominator.

Originally Posted by giorgio
Q1: pogono, what does represent?
https://en.m.wikipedia.org/wiki/Lorentz_factor

I hope it helps.

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Originally Posted by pogono
Dear macaw,
it makes sense. It is just fraction.
In math you may make fractions with any numbers except 0 in denominator.
To help you, here is an auxiliary question:
Q2: Does the metric (1) work for accelerated particles? Or not?

13. Originally Posted by DaveC426913
If you have a concern, use the report button, lower left.
Thanks DaveC426913

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Originally Posted by pogono
Dear macaw,
it makes sense. It is just fraction.
In math you may make fractions with any numbers except 0 in denominator.

https://en.m.wikipedia.org/wiki/Lorentz_factor

I hope it helps.
No, it doesn't, the website contradicts your attempt at defining (and, more seriously) using . Please answer the questions I put to you.

15. Pogono has been suspended, again, for rudeness and publicly accusing another member of being a sockpuppet, instead of using the report button or PM.
As it happens, the accused member does turn out to be a sockpuppet of a previously banned member and has been treated accordingly.

This thread will remain closed, if there is a good reason to reopen it, please use the report button.

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