# Zero-point Lorentz transformation (split from The twin Paradox revisited)

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42 minutes ago, Abouzar Bahari said:

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When the S is stationary and S’ is moving, what you are saying is that the term x'=(x-vt) in the Lorentz formula is in the Galilean-Newtonian mechanics and does not relate to SR. OK, this is true. In Newtonian mechanics, when we use the negative quantities for v, you will use x'=(x+vt), instead. Example:
x= 10 m
t= 2 s
v (S’ velocity) = 3 m/s
x'=(x-vt)= 10-(3)(2)=4 m
For v= -3 m/s --> x'=(x+vt)=10+(3)(2)=16 m
However, in Lorentz transformations, we are not going to use x'=γ (x+vt) and t'=γ(t+vx/c2) in the case that S’ is moving with the speed v to the left (for instance v = -108 m/s) and in any papers, texts, books, etc about the SR, nobody use such terms for Lorentz equations, in the case that S’ is moving to the left. Not Lorentz, nor Einstein, nor any other people.

All the times, everybody use the main formulas, whether the S’ frame is moving to the right or to the left. Have you asked of yourself, why?
That is because the Lorentz formulations have been invented to consider the light speed to be constant to c when it is propagated spherically for both S and S’ frame: metrics invariance for both S and S’. Before I make an example, I will derive the Lorentz equations when a light signal is propagated spherically :
𝑥 2 + 𝑦 2 + 𝑧 2 − 𝑐 2 𝑡2 = 𝑥 ′2 + 𝑦 ′2 + 𝑧 ′2 − 𝑐 2 𝑡 ′2 = 0  --> x=ct , x'=ct'
x'=γ (x-vt) -->  ct'=γ (ct-vt)
x=γ (x'+vt' ) -->  ct=γ (ct'+vt')
𝑦 = 𝑦’
𝑧 = 𝑧’
t=γt' (1+v/c)
t'=γt (1-v/c)
t'=γ^2 t' (1-v/c)(1+v/c)
γ=1/√(1-v2/c2 )

For instance, suppose the S frame is stationary and the S’ frame is moving to the left with a constant velocity v = 108 m/s. When the center of coordinates (zero point) of these frames is coincided with together, a light signal is propagated from this point spherically  (suppose in the figure 1, S' is moving to the left instead of moving to the right). At this moment, the clocks of both S and S’ observers which have already adjusted together, start to work. We want to calculate the light coordinate in both S and S’ frames after 2 ms.
In the S  frame:
t=2 ms
x=ct=3×108×2×10-3=6×10m =600 km

In the S’ frame: with employing the Lorentz transformations, we obtain:
x'=γ (x-vt)=1.06 (600-108×2×10-3)=424 km
t'=γ(t-vx/c2 )=1.41 s
Graphically, you can find that the quantities we have achieved with these formulas for the light signal coordinate for S’ is not true quantities for positive axes of x’. However, since the light is propagated spherically, for negative axes of x’, it becomes true. I mean when the
x=ct=-600 km --> x'=-424 km

Therefore, we can neglect the sign of x and v in Lorentz transformations and always use the main formulas, whether S’ is moving to the right or left.
But if you persist to use x'=γ (x+vt), when the S’ is going to the left, it is OK. However, when you reverse the formula to x=γ (x'-vt'), you must not to apply v reversal, as Dr. Rindler says, to make them symmetrical. If so, you would find γ=1/(1+v/c) which is less than 1 and so, your length would be elongated and time becomes faster.
Now, you can go and find something funnier.

First, the light speed is a universal constant c = 3*108 m/s. It is not equals to 1. So, when you use the c in the equations, if you want to simplify your mathematical equations, you can use c=1 instead. However, when you want it as a physical constant paprameter, you are not allowed to use c=1. For instance, in the Lorentz equations β= v/c is a number between 0 to 1. But if you put c=1, β= v/c is a number equals to v which could be much larger than 1. Therefore, it is wrong to use c=1 in the Lorentz formulas.
Second, as a physicist, you are supposed to simplify the equations not to make them more complicated by copy and paste other derivations of them for electrons inside the magnetic fields and we have from the Internet. Yes, absolutely there are other derivations of the Lorentz transformations in 4 dimensions. But, I am using the simple and completely applicable original Lorentz equations only for x direction, intentionally to explain why these equations are not symmetrical:
You have the equation x'=γ (x-vt), when you reverse it, you will find x=γ (x'+vt) , these two equations are not the same, so they are not symmetrical.
You have the equation t'=γ(t-vx/c2 ), when you reverse it you will find  t=γ(t'+(vx')/c2), these two equations are not the same, so they are not symmetrical.
We are not allowed to change the v sign, when we reverse the equation. Because we are performing just an arithmetic job, not changing the observer.
Third, after a PhD in nuclear physics and Ms. And Bs. In engineering and writing many outstanding papers that published in the ISI journals and teaching several years in the university and 10 years of hard studying about the SR (at least 200 papers and 20 books) and deep thinking and learning,  yes I can not understand the bullshits you add to my comments like "Λ(−v)Λ(v)A=IA means the symmetry of two equations" or γ' or other wrong statements of yours. But, what I understand is that I am talking to some young boys who ever in BS or lesser period and try to discuss with others without even study and learn their papers. This is crazy.
I taught I am discussing with some literate people not some dogmatic people who try to speak fast and loudly without even studying and hearing the words of the person in front of them. If I knew, I did not discuss with you never.

·         Please search in the internet and find the symmetry means. If you can prove that  Λ(−v)Λ(v)A=IA means the symmetry of two equations, I will accept your words, or else, please shut your mouth and first, study, then talk.

·         My attempt is not anti-relativity completely. I have accepted the invariant of the Lorentz equations, but, I do not agree with that they are symmetrical.

·         All the experimental tests agree with the above-mentioned claims. For instance, the atomic clock inside the moving high-speed airplane is dilated with the gamma factor, but the stationary atomic clock on the earth is not dilated. The researchers test the Lorentz formulas for the moving frames and get results for the Lorenz invariance of the inertial frames. However, they have ignored to test the Lorentz formulas from the view of the moving observer who thinks he is at rest according to what the SR says. Therefore, what they actually achieved is the Lorentz invariance not the symmetry of the inertial frames.

·         My paper after 5 month from its publication by a refereed journal was taken into account much more than I expected. In your forum, you mentors do not allow the others to speak. You just want to speak what you have learnt already in your books. But the real researchers are open- minded persons who do not think that all the matters in the books are true. They are finding the false theories. Just search how many famous scientists are completely or partially against relativity (you can find it in my paper).

·         About what you said I do not want to understand the negative value in the equation, read my answers to other.

·         But, whenever, some dogmatic people are dominant on the world of science, they could not be successful to talk and make their theories worldwide spreading. I do not want to say the journals should publish bullshits. But, I want to say the new theories if they are elaborated scientifically, must be published. Recently a published research showed that the velocity of the progress of science decreased rapidly in recent years. The reason is exactly those dogmatic people in the world of science today.

Unfortunately, the people like you, when they have not enough logic in their hands (mathematical or physical logic), try to humiliate the person against them. That is the method of not literate and not civilized persons and I am so familiar with such people. I again recommend you to study more and then come and discuss with honorable people. Just search my name then open your mouth and say bullshits.

-1.

You would be well advised to stop insulting people and clean up your own house. Neither one of us is "dominant in the world of science." As to you, you are nowhere near the world of science.

Reported.

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46 minutes ago, Abouzar Bahari said:

But if you put c=1, β= v/c is a number equals to v which could be much larger than 1. Therefore, it is wrong to use c=1 in the Lorentz formulas.

I am a relativity amateur, but this one is even clear to me: you should of course use the same dimension for velocity for v and c: both in m/s, or both in km/h. But if you set c = 1, then you should express v as a fraction of c. This is such a beginner's error, that I don't have to take the rest of your exposés seriously.

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14 minutes ago, Eise said:

I am a relativity amateur, but this one is even clear to me: you should of course use the same dimension for velocity for v and 😄 both in m/s, or both in km/h. But if you set c = 1, then you should express v as a fraction of c. This is such a beginner's error, that I don't have to take the rest of your exposés seriously.

I did not put c=1. others who were discussing with me did it, and I replied to them.

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12 minutes ago, Abouzar Bahari said:

I did not put c=1. others who were discussing with me did it, and I replied to them.

c can have any value you want just by choosing the length and time units accordingly, as @Eise told you.

33 minutes ago, Eise said:

you should of course use the same dimension for velocity for v and 😄 both in m/s, or both in km/h. But if you set c = 1, then you should express v as a fraction of c. This is such a beginner's error, that I don't have to take the rest of your exposés seriously.

Stop blaming your misunderstanding on others.

I also told you.

On 3/2/2023 at 12:03 PM, joigus said:

β=v in any system of units such as light-years per year, light-seconds per second, etc. That is, any system of units in which c=1 . I thought you understood that, @Abouzar Bahari.

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3 hours ago, Abouzar Bahari said:

But, what I understand is that I am talking to some young boys who ever in BS or lesser period and try to discuss with others without even study and learn their papers. This is crazy.
I taught I am discussing with some literate people not some dogmatic people who try to speak fast and loudly without even studying and hearing the words of the person in front of them. If I knew, I did not discuss with you never.

!

Moderator Note

You need to STOP making this personal! Others have focused on the physics and have told you where they have objections, and it's plain to see you haven't overcome these objections. Try engaging with the science instead of telling us how many papers you've had published (since that's a fallacious Appeal to Authority argument).

The members replying to you have been very specific about your math, and your response has been to wave the objections away and claim they don't know what they're talking about. That's not going to work here. You must deal with objections to your explanations when proposing non-mainstream science in the Speculations section. This is a science discussion forum, not your blog, and the difference is how you engage with those asking you for clarification.

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14 hours ago, joigus said:

-1.

You would be well advised to stop insulting people and clean up your own house. Neither one of us is "dominant in the world of science." As to you, you are nowhere near the world of science.

Reported.

shut your mouth and stop humiliation. I think you even not literate in the kindergarten level.

Just now, Abouzar Bahari said:

shut your mouth and stop humiliation. I think you even not literate in the kindergarten level.

reported as well.

12 hours ago, Phi for All said:
!

Moderator Note

You need to STOP making this personal! Others have focused on the physics and have told you where they have objections, and it's plain to see you haven't overcome these objections. Try engaging with the science instead of telling us how many papers you've had published (since that's a fallacious Appeal to Authority argument).

The members replying to you have been very specific about your math, and your response has been to wave the objections away and claim they don't know what they're talking about. That's not going to work here. You must deal with objections to your explanations when proposing non-mainstream science in the Speculations section. This is a science discussion forum, not your blog, and the difference is how you engage with those asking you for clarification.

Unfortunately, when I discussed and rejects their math and physics by strong math/physical logic and made them empty of any objection, they had to try humiliate and insult me. This behavior belongs to people who are not scientific, not literate and civilized. I have reported them. Please follow up this matter. Regards.

14 hours ago, joigus said:

c can have any value you want just by choosing the length and time units accordingly, as @Eise told you.

Stop blaming your misunderstanding on others.

I also told you.

False statement. Go and read what I wrote to you again.

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6 hours ago, Abouzar Bahari said:

6 hours ago, Abouzar Bahari said:

shut your mouth and stop humiliation. I think you even not literate in the kindergarten level.

reported as well.

Are you reporting yourself? No wonder you can't handle a sign inversion.

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8 hours ago, Abouzar Bahari said:

shut your mouth and stop humiliation. I think you even not literate in the kindergarten level.

Unfortunately, when I discussed and rejects their math and physics by strong math/physical logic and made them empty of any objection, they had to try humiliate and insult me. This behavior belongs to people who are not scientific, not literate and civilized. I have reported them. Please follow up this matter. Regards.

!

Moderator Note

Under the forum rules, disagreement is not considered an insult. However, telling someone they are not literate at the kindergarten level is.

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15 hours ago, swansont said:

!

Moderator Note

Under the forum rules, disagreement is not considered an insult. However, telling someone they are not literate at the kindergarten level is.

Mr, moderator, is not "As to you, you are nowhere near the world of science" an insult or humiliation  from your point of view????? if it is not, I have no other word with you nor this forum again.

17 hours ago, joigus said:

Are you reporting yourself? No wonder you can't handle a sign inversion.

Crazy persons, think other are crazy. So, shut up.

2 minutes ago, Abouzar Bahari said:

Mr, moderator, is not "As to you, you are nowhere near the world of science" an insult or humiliation  from your point of view????? if it is not, I have no other word with you nor this forum again.

Crazy persons, think other are crazy. So, shut up.

Or this one: "No wonder you can't handle a sign inversion.  "

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On 3/2/2023 at 12:37 PM, Abouzar Bahari said:

Λ is symmetrical when Λ(v)= Λ(v), which is not in Lorentz equations. See the term "Parity" in physics.

You do not understand what parity is. Parity is an involution, by definition. That is P2 = I.

That's because, if you change the sign of the coordinates, and then you change it again, you must get back to where you started.

Lorentz transformations, OTOH, are not. There is no reason why Λ2 should be the identity. Every symmetry transformation should be a representation of a group, for consistency. So Λ(v)Λ-1(v)=I. As it happens, Λ(v)Λ(-v)=I, so Λ-1(v)=Λ(-v). End of story as to the mathematics. If you are willing to present an experiment that contradicts this mathematics, that would be great.

Are we done here?

Another thing, Mr. Bahari. You can keep giving neg-reps every single time I take pains to explain to you why your idea cannot be right, if you are so inclined. I would like to see a reason why you're doing so, other than you thinking I'm 'illiterate.'

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A little bit more for you to ponder about, Mr. @Abouzar Bahari.

You might want to take a look at,

The fact that the transformations are symmetric --in the sense you mean them not to be-- is not an exclusive property of Lorentz transformations. AAMOF, Galilean transformations must comply with the same property you are in denial of. So, for slow velocities v, your argument is in trouble too:

$x'=x-vt$

$ct'=ct$

$y'=y$

$z'=z$

So, even Galilean transformations are inconsistent with what you say.

There is a powerful theorem that guarantees that the only relativity principles that can be consistent with a F=ma (second-order evolution equations) formulation of dynamics are the Galilean principle of relativity or the Einstein principle of relativity.

I rest my case. Or do I?

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2 hours ago, joigus said:

Are we done here?

I bloody well hope so! 😁

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10 minutes ago, joigus said:

A little bit more for you to ponder about, Mr. @Abouzar Bahari.

You might want to take a look at,

The fact that the transformations are symmetric --in the sense you mean them not to be-- is not an exclusive property of Lorentz transformations. AAMOF, Galilean transformations must comply with the same property you are in denial of. So, for slow velocities v, your argument is in trouble too:

x=xvt

ct=ct

y=y

z=z

So, even Galilean transformations are inconsistent with what you say.

There is a powerful theorem that guarantees that the only relativity principles that can be consistent with a F=ma (second-order evolution equations) formulation of dynamics are the Galilean principle of relativity or the Einstein principle of relativity.

I rest my case. Or do I?

I've suggested this four days ago (https://www.scienceforums.net/topic/128832-zero-point-lorentz-transformation-split-from-the-twin-paradox-revisited/?do=findComment&comment=1232116). It didn't help then. I am certain it will not help now.

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I've suggested this four days ago (https://www.scienceforums.net/topic/128832-zero-point-lorentz-transformation-split-from-the-twin-paradox-revisited/?do=findComment&comment=1232116). It didn't help then. I am certain it will not help now.

Thank you, @Genady. I must confess I didn't see your argument back then. If anything, the fact that we both concur on the same argument makes our case only more poweful.

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2 hours ago, joigus said:

You do not understand what parity is. Parity is an involution, by definition. That is P2 = I.

That's because, if you change the sign of the coordinates, and then you change it again, you must get back to where you started.

Lorentz transformations, OTOH, are not. There is no reason why Λ2 should be the identity. Every symmetry transformation should be a representation of a group, for consistency. So Λ(v)Λ-1(v)=I. As it happens, Λ(v)Λ(-v)=I, so Λ-1(v)=Λ(-v). End of story as to the mathematics. If you are willing to present an experiment that contradicts this mathematics, that would be great.

Are we done here?

Another thing, Mr. Bahari. You can keep giving neg-reps every single time I take pains to explain to you why your idea cannot be right, if you are so inclined. I would like to see a reason why you're doing so, other than you thinking I'm 'illiterate.'

You and others already have gotten your answers, scientifically. Try not to convince me by definitely WRONG statements. Λ-1(v)=Λ(-v) does not mean that two equations are symmetrical. For instance, 1/x is x-1, but it is not the symmetry of x or -x. Symmetry of signs means: x=x or x=-x. So, stop your false words. I am a nuclear physicist and work a lot with "parity" and such kind of terms in particle physics. So, please do not explain for me. I can not continue this discussion with you more, since you did not regard politeness in a scientific discussion. Please stop answering me. This is my post and I can hear from you anymore. Thanks.

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Mr. @Abouzar Bahari, I'm reinstating all the negative points you're giving everybody, just out of spite on your part, apparently.

3 minutes ago, Abouzar Bahari said:

Thank you. That's all I wanted to read from you.

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Posted (edited)
21 minutes ago, Abouzar Bahari said:

On 3/3/2023 at 7:33 AM, Abouzar Bahari said:

When the S is stationary and S’ is moving, what you are saying is that the term x'=(x-vt) in the Lorentz formula is in the Galilean-Newtonian mechanics and does not relate to SR. OK, this is true. In Newtonian mechanics, when we use the negative quantities for v, you will use x'=(x+vt), instead.

Which has nothing whatsoever to do with the comment you were responding to:

On 3/2/2023 at 8:26 AM, Lorentz Jr said:

Length contraction: $L' = {x'}_2 − {x'}_1 = \gamma(x_2 − vt)−\gamma(x_1 − vt)=\gamma(x_2 − x_1)=\gamma L$

Time dilation: $\displaystyle{\Delta t' = {t'}_2 − {t'}_1 = \gamma\left({t_2} −\frac{vx}{c^2}\right)−\gamma\left({t_1}−\frac{vx}{c^2}\right)=\gamma\left(x_2 − x_1\right)=\gamma\Delta t}$

No dependence on the sign of v. 😉

Edited by Lorentz Jr
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14 minutes ago, Abouzar Bahari said:

You and others already have gotten your answers, scientifically. Try not to convince me by definitely WRONG statements. Λ-1(v)=Λ(-v) does not mean that two equations are symmetrical. For instance, 1/x is x-1, but it is not the symmetry of x or -x.

You're confusing a group with a representation of a group. Any Abelian group can be represented by addition of parameters.

Example:

$e^{x+y}=e^{x}e^{y}$

The Lorentz group is represented multiplicatively on wave functions, but additively on other objects. Again, take a look at,

and it will dawn on you.

There's nothing else I can do for you here.

I'm sorry my help wasn't enough.

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10 hours ago, Abouzar Bahari said:

Mr, moderator, is not "As to you, you are nowhere near the world of science" an insult or humiliation  from your point of view?????

!

Moderator Note

Commentary on what one posts is fair game. If you were expecting a credulous audience, you have miscalculated.

As far as humiliation goes, that’s in the eye of the beholder.

10 hours ago, Abouzar Bahari said:

if it is not, I have no other word with you nor this forum again.

I guess this is goodbye, then

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Posted (edited)
13 hours ago, swansont said:
!

Moderator Note

Commentary on what one posts is fair game. If you were expecting a credulous audience, you have miscalculated.

As far as humiliation goes, that’s in the eye of the beholder.

I guess this is goodbye, then

Are you thinking I am crazy? As a moderator,you are supposed to regard justice, not to side a person/ group of persons. Their behavior was insult and humiliation, evidently (with no doubt). In addition, my paper has been verified already by very famous scientists like Prof. Hal Puthoff.  You and the other people here are not in a position to verify my paper and comments.

14 hours ago, Lorentz Jr said:

Which has nothing whatsoever to do with the comment you were responding to:

Nonsense, For sure.

Edited by Abouzar Bahari
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2 hours ago, Abouzar Bahari said:

my paper has been verified already by very famous scientists like Prof. Hal Puthoff.

Hello, I'm unable to find* a prof. Hal Puthoff using search engines, can you provide some reference to relevant work for this topic?

*) I found other titels and similar names but no professor.

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9 hours ago, Abouzar Bahari said:

Are you thinking I am crazy?

Did I say anything of the sort?

9 hours ago, Abouzar Bahari said:

As a moderator,you are supposed to regard justice, not to side a person/ group of persons. Their behavior was insult and humiliation, evidently (with no doubt).

I enforce the rules - critiquing what is posted is allowed.

Whether you find this insulting or humiliating is on you. Nobody else is responsible for your thin skin.

9 hours ago, Abouzar Bahari said:

In addition, my paper has been verified already by very famous scientists like Prof. Hal Puthoff.  You and the other people here are not in a position to verify my paper and comments.

If we’re not in a position to verify, one has to wonder why you posted here.

But consider this: if the Lorentz transforms aren’t symmetrical, then it must matter which frame is S and which is S’. You must get a different answer if you solve an identical problem by switching S and S’. But that doesn’t happen - you get the same result.

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Posted (edited)

I am pretty sure he means Harold E. Puthoff. He is also known as 'Hal Puthoff'. He has some articles on 'zero-point-something':

Quote

Peer-reviewed papers
Bernhard Haisch; Alfonso Rueda; HE Puthoff (February 1994). "Inertia as a zero-point-field Lorentz force". Physical Review A. 49 (2): 678–694. Bibcode:1994PhRvA..49..678H. doi:10.1103/PHYSREVA.49.678. ISSN 2469-9926. PMID 9910287. Wikidata Q21709034.
Harold E. Puthoff (1 November 1989). "Source of vacuum electromagnetic zero-point energy". Physical Review A. 40 (9): 4857–4862. Bibcode:1989PhRvA..40.4857P. doi:10.1103/PHYSREVA.40.4857. ISSN 2469-9926. PMID 9902742. Wikidata Q77842791. (erratum)
Harold E. Puthoff (1 March 1989). "Gravity as a zero-point-fluctuation force". Physical Review A. 39 (5): 2333–2342. Bibcode:1989PhRvA..39.2333P. doi:10.1103/PHYSREVA.39.2333. ISSN 2469-9926. PMID 9901498. Wikidata Q77838067.
Harold E. Puthoff (1 May 1987). "Ground state of hydrogen as a zero-point-fluctuation-determined state". Physical Review D. 35 (10): 3266–3269. Bibcode:1987PhRvD..35.3266P. doi:10.1103/PHYSREVD.35.3266. ISSN 1550-7998. PMID 9957575. Wikidata Q63170624.

Puthoff is mostly known as a parapsychologist...

On 3/5/2023 at 4:02 PM, Abouzar Bahari said:

I am a nuclear physicist and work a lot with "parity" and such kind of terms in particle physics.

Well, if I look at Google Scholar, there is more about drilling for petroleum, than anything else:

We will not miss him.

Edited by Eise
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Posted (edited)
On 3/6/2023 at 11:00 AM, Ghideon said:

Hello, I'm unable to find* a prof. Hal Puthoff using search engines, can you provide some reference to relevant work for this topic?

*) I found other titels and similar names but no professor.

Hello. Use the following link to know more about Prof. Harold E. (Hal) Puthoff:

On 3/6/2023 at 4:27 PM, swansont said:

Did I say anything of the sort?

I enforce the rules - critiquing what is posted is allowed.

Whether you find this insulting or humiliating is on you. Nobody else is responsible for your thin skin.

If we’re not in a position to verify, one has to wonder why you posted here.

But consider this: if the Lorentz transforms aren’t symmetrical, then it must matter which frame is S and which is S’. You must get a different answer if you solve an identical problem by switching S and S’. But that doesn’t happen - you get the same result.

You are supposed to regard justice for everyone. They started to humiliate and insult me. I had to answer their impoliteness and bad-tempered behavior. YOU ALSO TRY TO SPEAK RUDELY BY SAYING "YOUR THIN SKIN". This is wrong. Again, you also try to humiliate others. Do not such unscientific behavior.

If you read my paper, I have made it clear that the inertial frame, which is moving in relation to the ZPF, is tolerating the Lorentz transformations and the inertial frame which is at rest, in relation to the ZPF, is not supposed to be transformed by Lorentz equations.

On 3/6/2023 at 6:46 PM, Eise said:

I am pretty sure he means Harold E. Puthoff. He is also known as 'Hal Puthoff'. He has some articles on 'zero-point-something':

Puthoff is mostly known as a parapsychologist...

Well, if I look at Google Scholar, there is more about drilling for petroleum, than anything else:

We will not miss him.

My BS. is Mining Engineering, M.S. is Petroleum Engineering and PhD is Nuclear Physics. I am also studying Ms. in Genetics (Biology). I have several researches about advanced mathematical methods like Genetic algorithm, Phase logic, Monte Carlo methods, advanced optimizations (like Trust-region), Neural Networks and etc. in Petroleum Engineering and Nuclear physics (for those people who said to me that you do not know the arithmetic signs and they recommend me to work on mathematics 😂). However, as I said, I have worked on SR and GR much more than the other researches (about 1/4 of my life).

Edited by Abouzar Bahari

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