# Thread: Deriving space-time in four-dimensional Euclidean space with no time and dynamics

1. Ans
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Originally Posted by Reality Check
I was very clear. You got equations that look like the Lorentz transformation. The equations are not the Lorentz transformation because the Lorentz transformation does not exist in Euclidean space. The Lorentz transformation exists in Minkowski space. This is textbook special relativity.
Thank you for reminding to me textbooks, but I think I know the textbooks very well.
Also I remember that it is not possible to build Lorentz-like transformation in Euclidean space, by exactly same reason as Lorentz transformation. Difference between Lorentz-like transformation and Lorentz transformation is only in unknown value of speed in Lorentz-like transformation.
If take all postulates of SR, remove postulate about maximum value of speed is equal to speed of light, we would get same transformation of spacetime as Lorentz transformation except value of speed would be unknown.
However, if remove key assumption of that prove of impossibility to build Lorentz transformation in Euclidean space, that prove would not be applicable. I already wrote about it, just several posts above.
And, after removal of requirements for events exists in all frames of references, it is possible to build Lorentz transformation in Euclidean space. As I already mathematically proved.

2. Ans
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Originally Posted by Reality Check
My questions are based on the simple fact that time exists and you still have not derived time from a (x,y) plane with 2 fixed points or in any other way. Your ATM idea thus falls at the first hurdle and the rest is almost moot. I pointed out a couple of other obvious errors.

The "intelligent observer/emergent space-time" story in this post did not derive time.
Am I understand correctly that you ready to consider only time as fundamental phenomena and nothing else?

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Originally Posted by Ans
Am I understand correctly that you ready to consider only time as fundamental phenomena and nothing else?
You are to understand that time exists in the real universe but not in your ATM idea. That makes you ATM idea not applicable to this universe unless you can derive time and show that an observer with no time can measure changes as in my questions.

IF01: Give your definition of velocity that has no time, Ans, or derive the definition of velocity that we use that has time from your theory.
IF02: How can your observer who is in a space with no time measure a change in x (the dx in velocity) when all you have is 2 unchanging points, Ans?
Last edited by Reality Check; 2020-Apr-21 at 09:06 PM.

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Originally Posted by Ans
Thank you for reminding to me textbooks, but I think I know the textbooks very well.
Also I remember that it is not possible to build Lorentz-like transformation in Euclidean space, by exactly same reason as Lorentz transformation. Difference between Lorentz-like transformation and Lorentz transformation is only in unknown value of speed in Lorentz-like transformation. ...
You need to review the textbooks again. SR and the Lorentz transformation exist in Minkowski space. That is why it is impossible to derive the Lorentz transformation in Euclidean space. Whatever equations you get in Euclidean space are not the Lorentz transformation and not anything to do with SR.
IF05: Cite and quote the textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space" (when that is what you do in your PDF!), Ans.

You are making an analogous error as in my IF04 question:
IF04: Give your source that states the pseudo-Riemann manifold used in GR is a curved hyperplane hypersurface, Ans.
SR needs a Minkowski space. GR needs a pseudo-Riemann manifold. You cannot derive either from things that are not the appropriate mathematic space. The GR error is slightly worse because you do not even have a mathematical definition of your hypersurface with the fundamental properties needed by GR.
Last edited by Reality Check; 2020-Apr-21 at 09:15 PM.

5. Ans
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Originally Posted by Reality Check
You need to review the textbooks again. SR and the Lorentz transformation exist in Minkowski space. That is why it is impossible to derive the Lorentz transformation in Euclidean space.
No, reason is different. It looks as you need to read textbooks…
More below.

Originally Posted by Reality Check
Whatever equations you get in Euclidean space are not the Lorentz transformation and not anything to do with SR.
IF05: Cite and quote the textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space" (when that is what you do in your PDF!), Ans.
With easy. It is enough to just copy-paste first reference from article: S. Hawking, J. Ellis, The Large Scale Structure of Spacetime, published by Mir, 1977
If you would find English version, look at chapter 5 (if I remember number correctly). In that part, there is prove that it is impossible to have inscribed hypersurface with signature of metric different from signature of space metric.
Signature of metric for 4d Euclidean space is (1,1,1,1). Signature of metric for Minkowski space, for Lorentz transformation, is (1,1,1,-1). Signature of metric for Lorentz-like transformation is (surprise-surprise) (1,1,1,-1)
So, it is impossible to build hypersurface in Euclidean space with metric (1,1,1,-1) , and it affect both Lorentz-like transformation and Lorentz transformation. Lorentz transformation is just one of Lorentz-like transformations

By the way, if ask how I do that is proven as impossible to do – I already answered it.

6. Both of you stop telling each to read text books and discuss this politely.

7. Ans
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Originally Posted by Reality Check
You are to understand that time exists in the real universe but not in your ATM idea. That makes you ATM idea not applicable to this universe unless you can derive time and show that an observer with no time can measure changes as in my questions.
So, you say that time exists in real Universe and looks as you assume it is fundamental phenomenon.
Hmm. I see time is really exists and it is observable, but I have not seen proves that time is fundamental phenomenon.
And it looks as you assume that time is fundamental phenomenon. It was never proven.
Second positivism (mainstream) says that information derived from sensory experience, interpreted through reason and logic, forms the exclusive source of all certain knowledge. But looks as you say that time is fundamental phenomenon without any evidence for it.
So, seems as it is your ATM idea. Using ATM idea against another ATM idea to protect mainstream looks quite strange.

8. Originally Posted by Ans
So, seems as it is your ATM idea. Using ATM idea against another ATM idea to protect mainstream looks quite strange.
Ans,

If you don't provide some real, substantive support for your claims, this thread will be closed. Get to work. Derivations, please.

9. Ans
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Well.
As example, I can use thermal time hypothesis of Rovelli, one of authors of LQG.
Is time in the hypothesis fundamental or no is quite fuzzy. He use automorphism to build time. And the paper is published, quite well known, and considered as scientific.
Another example is M.Tegmark, with his mathematical universe. Again, question of time in his hypothesis is quite fuzzy. Quite famous work, again is time fundamental or no is questionable.
So, based on examples above, it is clear that there is no prove that time is fundamental phenomenon. It is in mainstream, no doubt. But it was not proven.

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Originally Posted by Ans
So, you say that time exists in real Universe and looks as you assume it is fundamental phenomenon.
No. I say time exists in real universe. Full stop. Period. But in your ATM idea there is no time. Thus your idea does not apply to the real universe until you can derive that time exist. Thus my questions.

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Originally Posted by Ans
....With easy. ...
You wrote: Also I remember that it is not possible to build Lorentz-like transformation in Euclidean space, by exactly same reason as Lorentz transformation
IF05: Cite and quote the textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space" (when that is what you do in your PDF!), Ans.

It is obviously possible to build an equation that looks like the Lorentz transformation in Euclidean space because you did it. The obvious error still is the textbook physics that the Lorentz transformation exists in a Minkowski space. A Euclidean space has a signature of (+ + + +). A Minkowski space has a signature of (+ + + -) or (+ - - -) depending on an author's preference. They are different.

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Originally Posted by Ans
Well.
As example, I can use thermal time hypothesis of Rovelli, one of authors of LQG.
You cannot use a hypothesis that is irrelevant to your ATM idea. The Thermal time hypothesis is about the different concepts of the flow of time in QM and GR and how to reconcile them. Rather than having an assumed physical time-flow in QFT, they propose that the physical time-flow will emerge from the thermodynamics.
Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories (1994) by A. Connes, C. Rovelli.

13. Ans
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Originally Posted by Reality Check
You cannot use a hypothesis that is irrelevant to your ATM idea. The Thermal time hypothesis is about the different concepts of the flow of time in QM and GR and how to reconcile them. Rather than having an assumed physical time-flow in QFT, they propose that the physical time-flow will emerge from the thermodynamics.
Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories (1994) by A. Connes, C. Rovelli.
I read the work, years ago.
I use the hypothesis not in support of my idea, but to show that question of what time is, not so obvious as some may think.

14. Ans
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Yes, I did it, and it is one of fundamental results of my theory.
I not know any other theory that allows to build Lorentz-like transformation in Euclidean space.

Originally Posted by Reality Check
The obvious error still is the textbook physics that the Lorentz transformation exists in a Minkowski space. A Euclidean space has a signature of (+ + + +). A Minkowski space has a signature of (+ + + -) or (+ - - -) depending on an author's preference. They are different.
Really, you asking again? You think that signature for metric for Lorentz-like transformation is (+ + + +)?

15. Ans
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Originally Posted by Reality Check
No. I say time exists in real universe. Full stop. Period. But in your ATM idea there is no time. Thus your idea does not apply to the real universe until you can derive that time exist. Thus my questions.
There is time in my theory, and I already shown it.

For that example with plane (x,y) with defined on the plane field f(x,y)=x+y
How to transform it from timeless 2d plane (x.y) to one dimensional space z with time t: (z,t):

Take vertical line x=2.
Value of field for any parallel line at point y at distance l from x=2 (x=2+l, y=y) would be f(x,y) = (2+y) +l
Next, I set z=y, t=l
I use the distance l as time.
What is value of field at point z at time t? f(z,t) = f(z, t=0) + t
You may see, field is changing over time.
Equation of evolution looks as it should look: time is parameter of evolution in equation.
So, (x,y) was transformed to (z,t), where t is time.

I see only several possible outcomes from the derivation of spacetime:
1. There is some error in the derivation. But the derivation is so simple, that I not see where one can find error
2. “There is no time here” – for the case, with shown above math, it would be simply rejection from considering the proposed time as time on basis of philosophical beliefs. It have no relation to science.
3. Yes, there is time here, and it can be considered for consequences.

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18. Ans
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Originally Posted by Reality Check
I not understood. Is IF05 your question or you not asking question?
Also, it is not clear for me why you asking it. You think that signature for spacetime for Lorentz-like transformaion is same as for Euclidean space?
Look at signature for spacetime for Lorentz-like transformation. Its signature can be derived in second, just from glance. Compare its signature with Euclidean space, and see result.

By the way, idea to build Lorentz-like transformation in Euclidean space is obviously against mainstream. It must be clear for anyone, who consider himself as physisist.

19. Originally Posted by Ans
If you did answer, please provide a link to the post in which you cited a textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space."

20. Ans
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Originally Posted by Reality Check
A distance between points in Euclidean space is never a time.
Any prove for your statement? I see only philosophical belief in response to my mathematical derivation of spacetime.

No, it was answered. In response to my math, I see only words, not backed by any scientific evidence.

Originally Posted by Reality Check
Epic question.
Originally Posted by Ans
Hmm. In mainstream science it is not curved hyperplane or curved hypersurface, I remember courses on general relativty and on differential geometry.
In my theory it is, and I shown it results in same equations as EFE.
Second, it is one of results of my theory. So, in order to prove my against mainstream theory, you asking where in mainstream literature the theory was proved? Fantastic.

21. Ans
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Originally Posted by PetersCreek
If you did answer, please provide a link to the post in which you cited a textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space."
Link to post in which I cited a textbook that states it is not possible to build inclined hypersurface with metric different from outer space:
Originally Posted by Ans
With easy. It is enough to just copy-paste first reference from article: S. Hawking, J. Ellis, The Large Scale Structure of Spacetime, published by Mir, 1977
If you would find English version, look at chapter 5 (if I remember number correctly). In that part, there is prove that it is impossible to have inscribed hypersurface with signature of metric different from signature of space metric.
Signature of metric for 4d Euclidean space is (1,1,1,1). Signature of metric for Minkowski space, for Lorentz transformation, is (1,1,1,-1). Signature of metric for Lorentz-like transformation is (surprise-surprise) (1,1,1,-1)
So, it is impossible to build hypersurface in Euclidean space with metric (1,1,1,-1) , and it affect both Lorentz-like transformation and Lorentz transformation. Lorentz transformation is just one of Lorentz-like transformations
If someone not understood that is written above (and it would means insufficient level of knowledge in physics). The textbook explain, why it is not possible to build hypersurface with Minkowski spacetime metric in Euclidean space. Lorentz transformation is one of Lorentz-like transformations, just different speed. Signature of metric is same.

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Originally Posted by Ans
...
I did not ask a question in what you replied to. The facts are:
One more time: SR and the Lorentz transformation exist in Minkowski space which is not Euclidean space. SR and the Lorentz transformation cannot be derived purely from Euclidean space.
Last edited by Reality Check; 2020-Apr-26 at 09:33 PM.

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Originally Posted by Ans
Any prove for your statement? I see only philosophical belief in response to my mathematical derivation of spacetime. ...
There is no mathematical derivation of spacetime in you ATM idea as the lack of actual answers to my questions shows. Wishful assertions are not a derivation.
IF01: Give your definition of velocity that has no time, Ans, or derive the definition of velocity that we use that has time from your theory.
IF02: How can your observer who is in a space with no time measure a change in x (the dx in velocity) when all you have is 2 unchanging points, Ans?[/QUOTE]

IF04: Give your source that states the pseudo-Riemann manifold used in GR is a curved hyperplane hypersurface, Ans (The EFE are defined in a pseudo-Riemann manifold thus you cannot derive them without a pseudo-Riemann manifold which you agreed with when I did my Euclidian space "derivation").
I have added why your assertion that you derived the EFE is extremely.

No proof is needed. You stated that you start with a (x,y) plane with no time. By your definition, the distance between any 2 points is a spacial distance.

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Originally Posted by Ans
No you did not. You partially answered it with a citation of a book that I would have to buy and no quote from the book.
IF05: Cite and quote the textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space" (when that is what you do in your PDF!), Ans.

What you wrote about what may be Chapter 5 of "S. Hawking, J. Ellis, The Large Scale Structure of Spacetime, published by Mir, 1977" may be that it states you cannot do what you did ("it is impossible to have inscribed hypersurface with signature of metric different from signature of space metric").. Also an obvious error that you have a "Signature of metric for Lorentz-like transformation is (surprise-surprise) (1,1,1,-1)". You started with a Euclidean space. You ended with a Euclidean space. You do not have any kind of Lorentz transformation because your equations are in Euclidean space with a metric signature of (1,1,1,1).
Last edited by Reality Check; 2020-Apr-26 at 09:46 PM.

25. Seems to be something of a language barrier going on.

By definition, hyperspaces exist in Euclidean space.

I really cannot discern the actual claim out of the broken english.

26. Ans
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Seems to be something of a language barrier going on.

By definition, hyperspaces exist in Euclidean space.

I really cannot discern the actual claim out of the broken english.
I not see language barrier. Reality_check seems as understand that I claim as done. He not understand my ideas, but seems as reason is different than language barrier.

I spent quite a lot of time in US, in business trips. Once I was on 3 month duration business trip. Based on experience, I can say I can freely talk in english, I have large vocabulary, but my grammar needs improvement.

I will write answer to Reality_check tomorrow, no time today.

27. Originally Posted by Ans
I will write answer to Reality_check tomorrow, no time today.
Ans,

You should have answered the question long before now because you've been asked several times. I've also warned you that you must answer. If you do not, you will receive a heavy infraction.

28. Ans
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It looks as in the discussion, I present both positions: position of mainstream and position of my theory. And seems as in the discussion, only I correctly present position of mainstream.
Why I think so?
I think so, because in the discussion, only I use scientific arguments from mainstream.
One only scientific argument in the discussion, about impossibility to have inscribed hypersurface with Minkowski metric in Euclidean space was proposed by me. Actually, it was considered in my article and it was shown why and how I was able to do what was looked as proven as impossible to do.
Mainstream not tell us: “A distance between points in Euclidean space is never a time”. No, it tell us: “distance between points in Euclidean space cannot be time because …”
And in the “because” part, there is clear mathematical prove of the statement. The prove is based on some assumptions. One of the assumptions is not applicable to my theory, and it make the statement not applicable to my theory.
So, when someone says “A distance between points in Euclidean space is never a time” it was either written from position of teacher or from position of author of such hypothesis.
If it was written from position of teacher – thanks, but I have degree in physics, so I have reasons to think I know physics well.
Why it is hypothesis, if it was written not from position of teacher? Because in mainstream, the statement was proven on basis of some assumptions.
If say “A distance between points in Euclidean space is never a time” with assumptions it applicable to everything, it means go beyond proven area. So, it means new hypothesis, not proven in mainstream.
So, Reality_Check here wrote some new hypothesis. May I ask for prove of the hypothesis?

29. Ans
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Originally Posted by Reality Check
No you did not. You partially answered it with a citation of a book that I would have to buy and no quote from the book.
We are talking about something written in textbooks, right?
If there is no access to one particular textbook, may be it should be in many other textbooks? Is it logical?
One only reason why I added in my article citation to that particular textbook is I read it right at time I need to make reference about that signature to something.
My search in google gave me lots of other textbooks with same statement, and it took less than a minute.
I think such knowledge should be known by anyone, who consider himself as specialist in SR or GR.
I remember I heard it during lectures on special relativity on first course, faculty of physics.

Originally Posted by Reality Check
IF05: Cite and quote the textbook that states it is "not possible to build Lorentz-like transformation in Euclidean space" (when that is what you do in your PDF!), Ans.

What you wrote about what may be Chapter 5 of "S. Hawking, J. Ellis, The Large Scale Structure of Spacetime, published by Mir, 1977" may be that it states you cannot do what you did ("it is impossible to have inscribed hypersurface with signature of metric different from signature of space metric").. Also an obvious error that you have a "Signature of metric for Lorentz-like transformation is (surprise-surprise) (1,1,1,-1)". You started with a Euclidean space. You ended with a Euclidean space. You do not have any kind of Lorentz transformation because your equations are in Euclidean space with a metric signature of (1,1,1,1).
You know, language of physics is math. I mathematically proved all my statements. It may contains errors (I not know any), but it is necessary to use relevant language (math) to try to refute it.

Interesting, you not said anything about signature for Lorentz-like transformation. In posts before it looked as you think it have same signature as Euclidean, it was so obvious against math.

30. Ans
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Originally Posted by PetersCreek
Ans,

You should have answered the question long before now because you've been asked several times. I've also warned you that you must answer. If you do not, you will receive a heavy infraction.
I think I answered every question and many times.
May you provide question, which you think was not answered?

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