1. Originally Posted by SergeMak
Interestingly, though, that some scientific ideas were primarily invented by sci-fi writers and only then became adopted by physicists. Such a thing has happened with the idea of relativistic space-time. The Einstein-Minkovsky concept is that time is just another dimension of relativistic space-time unity. But this idea was elaborated by H.G. Wells in his "The Time Machine". I used too think that Wells wrote that novel under the impression of relativistic ideas of Einstein, but in reality, the book was written a few decades before Minkovsky and Einstein developed their time-space concept. And the book was based on a short story published even several decades earlier than the novel. So it looks like Wells knew intuitively about time-space half a century before scientists did!
I don't think so. Speculations about "fourth spatial dimension" were quite common in the time of Wells (almost as now). The Idea to put time to the same coordinate system as spatial coordinates was obvious and trivial if not for Euclid then for Descartes for sure (remember those school graphs of distance vs time). What stated Wells is "look, they are similar: all are measurable. If we can change our coordinate in space maybe with some device we can arbitrarily change our time coordinate". What came from Einstein's mathematics is: "time and space positions are not independent values but mixed up in a special way". I don't see why it can be the same.

2. Speculations about "fourth spatial dimension" were quite common in the time of Wells (almost as now). The Idea to put time to the same coordinate system as spatial coordinates was obvious and trivial if not for Euclid then for Descartes for sure (remember those school graphs of distance vs time). What stated Wells is "look, they are similar: all are measurable. If we can change our coordinate in space maybe with some device we can arbitrarily change our time coordinate". What came from Einstein's mathematics is: "time and space positions are not independent values but mixed up in a special way". I don't see why it can be the same.
I am sorry but I cannot agree with you. What Wells really said was: "There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it". It's a citation from the book. So he didn't say about putting time in the same coordinate system as space, he really introduced the idea that time is just another dimension of space.
On the other hand Minkovsky and Einstein haven't just showed that "time and space positions are not independent values but mixed up in a special way", because that was very obvious much earlier. Actually if the time and space coordinates had not been dependent on each other, the world would have become a chaos, for the mutual positioning of objects in space at certain moments of time could have been impossible. No, what Minkovsky and Einstein really invented was the assertion that time and space not just depend on each other, but that they are unity, they are 4 sides of the same physical phenomenon.

3. I believe that the citation was a metaphor to emphasize what was written below. If you insist on understanding it literally than it is just wrong - time is not exactly the same as spatial dimensions in either Newton's or Einstein's description. As for "not just depend on each other, but that they are unity" - I don't see the difference. Anyway it looks like philosophy rather than physics. Philosophy can not predict results of physics - their subjects are different. If Wells described some relativistic phenomena in his novell then one would be able to speak about predictions. But all we have is an obscure sentence to meditate at. Точно так же Иван Грозный, сказавший "я тебя насквозь вижу" IMHO не является предсказателем изобретения рентгеновского аппарата.

4. As for "not just depend on each other, but that they are unity" - I don't see the difference.
The difference is tremendous, although quite difficult to grab. If you reduce the number of space dimensions to 2 it would not be hard to imagine time-space as a brick or a bar of butter or cheese where two coordinate planes represent space and 3rd stands for time. If a physical point moves in space it draws a line inside that bar of butter. If I take a knife and cut that cheese I will get a number of 2-dimensional sections with a point in it which stand for momentarily space coordinates of the physical point in a known point in time. The difference between Newtonian absolute space and time and Minkovsky perception of the space-time model is that Newtonian concept treats time as an absolute entity completely orthogonal to space. In other words you can cut the butter only at right angle to the space dimensions and you'll always get sections of the same shape with the same coordinates of the moving point. It's not the case with the space-time concept. Time is not absolute any more. You can cut the bar at different angles and get different coordinates of the moving point at the same moments of time in different inertial coordinate system moving with different speeds relative to each other. And there is no such a thing as the absolute coordinate system. More than that, if the moving object is not just a physical point but has distinct space sizes - length, width, height you will notice that tese sizes are different from the point of view of different coordinate systems. So it shows that time is not absolute, it can be actually converted into space and vice-versa. And if time can be turned into space and vice-versa it means that time and space have the same nature, they are made of the same fabric, if you excuse this parable, and they create unity.
Anyway it looks like philosophy rather than physics. Philosophy can not predict results of physics - their subjects are different.
Well, you have a point, but let me state my opinion that any physical theory is based on some philosophical concept. Newton was a devoted Сhristian and that laid an imprint on his perception of the physical world. Absolute Time orthogonal to Absolute Space, the main coordinate system attached to them - all this concepts are in total concordance with the idea of Absolute God. Einstein on the other hand was a follower of Mach's philosophy and it shows in his theories.
Well, unlike faster-than-light travel, it doesn't blatantly violate known laws of physics
The problem is, the impossibility of faster-than-light travel is not explained by any known law of physics. It's postulated "as is" and the whole physics theory is built upon that postulate. It's overall accepted, it's proved by innumerable experiment and observations but it never has been plausibly explained.
On the other hand, today's real-world physics predicts that IF Einstein-Rosen bridges actually exist at all, anything much larger than an electron would be crushed into "singularity" while attempting to pass through the wormhole. So, science-fiction which depicts ships going back and forth through wormholes is essentially "stealing" a valid concept from modern physics and using it in Magical and unrealistic way -- they might as well forget any pretense of science and solve the problem of interstellar travel by using the Floo Spell from Harry Potter!
I agree, but please remember, that however modern and strange and complicated the relativity may seem in fact it is a classical physics theory in the sense that it isn't a quantum theory. So nowadays it is perceived as outdated and needs to be redesigned in order to be built in the modern quantum perception of the world. As for the quantum theory, it opens doors to almost boundless flight of fantasy and speculations.

5. Originally Posted by SergeMak
In other words you can cut the butter only at right angle to the space dimensions and you'll always get sections of the same shape with the same coordinates of the moving point.
Why? I can cut as I like and write proper mathematical formula in new arbitrary coordinates. The model doesn't deny such a possibility even if I don't see any practical reason to do it. There is no factor to translate seconds into meters (like c in relativity) but i can take it arbitrarily. Why not? There is nothing unusual in such approach. For example it is used in the experimental design math apparatus - all parameters (different values in different units) are treated as dimensions and available range is normalized to get [-1..1] in all dimensions. And here you are - we have an isotropic space and can do whatever we like - rotate and so on.

Originally Posted by SergeMak
Well, you have a point, but let me state my opinion that any physical theory is based on some philosophical concept. Newton was a devoted Сhristian and that laid an imprint on his perception of the physical world. Absolute Time orthogonal to Absolute Space, the main coordinate system attached to them - all this concepts are in total concordance with the idea of Absolute God. Einstein on the other hand was a follower of Mach's philosophy and it shows in his theories.
People come to their conclusions with a different ways. One can use mneumonics or philosophy whichever he likes - that's his personal problem. Creativity is hardly formalizable. Newton presumably formulated gravity law as a result of an apple strike but i doubt that if it was a pear the law would be different. Natural sciences are objective - even if a scientist use formulations that may reflect his personality the essence is independent on that. Humans don't "invent" natural laws - they discover.

6. Why? I can cut as I like and write proper mathematical formula in new arbitrary coordinates. The model doesn't deny such a possibility even if I don't see any practical reason to do it.
No, you can't. You don't understand the allegory and you are too hasty. It probably partly comes from the fact that contemporary school program in physics doesn't give the classical Newtonian perception in its original way, as it was described in his "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy). You can arbitrary choose the direction of spacious axes and the beginning reference point, but you are not free to choose the direction of the time axis. And the simultaneous events always stay simultaneous in any Newtonian reference system, because Newtonian Time is absolute. Newton has even attached a reference system to his Absolute Time and Absolute space. Regarding my allegory it means that you can cut the bar only at right angle. But contemporary pupils are not given this concept, they are told from the very beginning that any inertial reference system is equally good, but it isn't a Newtonian concept.
The case of cutting the space-time bar at angles other than the right one is also not arbitrary, the angle depends on the velocity of my reference system relative to other inertial systems, so you are not free to "cut as you like". But if you move you must cut at angles other than right. Then, if you imagine that a trace in a bar was made not by a tiny point, but a ball with a perceptible diameter, you'll find that the section of this trace may not be round but oval. It means that moving objects change their sizes relative to inertial reference systems other than their own. And the more the difference in velocity of the systems is, the more is the change in the size of the objects. This can never happen in Newtonian absolute space and time. Another allegory is that if we have traces of two events in the space-time bar, which can be described as two wholes in a piece of cheese they may appear on the same plane of one section and in another section there can be only one of them. So, as the sections along the time axis represent the moments of time it means that two events simultaneous in one reference system are not simultaneous in another and it also doesn't make sense from Newtonian point of view, but it makes sense from the relativistic point of view, and once again it shows that you are not free to "cut as you like" the classical Absolute Time and Space.
Natural sciences are objective - even if a scientist use formulations that may reflect his personality the essence is independent on that. Humans don't "invent" natural laws - they discover.
The history of science disproves this assertion. A very demonstrative example is the change in physicists' perception of the nature of light. Huygens believed that light is oscillation of ether, Newton reckoned that it's a stream of particles, corpuscles. Both theories had their strong and weak sides and in different times each of these theories experienced flowering and decay.
The truth is we study reality not directly as it is, but designing descriptive mental models that can fall near or far from the truth. The more we study Nature the more complicated our models became, the nearer to the truth we get, but I rather doubt if the definitive description of Nature is possible let alone there is no doubt we are only at the very beginning of the process of cognition.

7. Originally Posted by SergeMak
No, you can't.
Still I insist that I can. It is not about physics - it is about mathematics. Well, OK, no matter. All I question is why one kind of anisotropy makes "unity" while particular case of the same anisotropy (with c=infinity) doesn't.

Originally Posted by SergeMak
The history of science disproves this assertion.
For me it is not an assertion. It is a definition of term "natural sciences". What is behind objectivity is behind science. Natural laws are not speculative descriptions like "oscillations of ether" or whatever. Natural laws are mathematics plus limitations that work - as far as they work. If we know how to calculate the results corectly - we know the law. All the rest are just ways to help human brains manipulate it - the perception as you say. Perception of the science in not a science itself.

If you remember all of that was because I disagree that "Time machine" was a "prediction" Einstein's RT. It is just your way of perception came in resonance with a sentence by Wells. Some personal associations.

Originally Posted by SergeMak
The truth is we study reality not directly as it is, but designing descriptive mental models that can fall near or far from the truth. The more we study Nature the more complicated our models became, the nearer to the truth we get, but I rather doubt if the definitive description of Nature is possible...
Yep. Cognition means building generalized models. Model is a simplified description of the object. If the description is complete it is not a model any more. Again terminology...

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