Look, help me understand the implications of this.

Closed time-like curves is a product of general relativity math. That does not mean they are real.

Differential equations could have multiple solutions. Solution of differential equation is a function. So, there could be many functions that fit some theory that uses differential equation, but it could be that only few of them really occur in nature.

In one of my businesses I earn money from practical use of theory with differential equation as its core. (Sorry, I will not disclose exact details, since it could be a way to deanonymise me :) ) To use this theory practically, I have to find solution and use that solution to get result that could be practically verified. It is easy (well, not very easy, but whatever) to get a dozen of solutions, but in practice only few really works and give correct practical results that equal to what I get in practice. All other solutions, being mathematically correct either collapse when things come to real data, either produce complete garbage.

Meanwhile same thing happens with all that "new particle search" thing. Somebody find yet another solution that mean existence of new particle, people spend millions and years to check it, and find out that this solution just don't work in reality, being mathematically correct.

Hopefully, checking solution in my area don't need millions and years, and I don't really interested in producing more solutions, since those I already found works good. May be they are not insanely perfect, and may be there could be better solutions, but customers are fully satisfied, because they just work as intended. They do the job, so no need to search and research new "particles" or "closed timelike curves" for me. Unlike all those theoretical scientists who make money doing that.

Mathematical solution does not mean that it even have some sense. Math is a language for describing nature. And as in any language you could create perfectly grammatically correct sentencies that don't have any sense at all. Same with math.

Adding to that questionability of general relativity in whole, we get something like word salad expressed in non-existing language.

Also, who told that travelling through wormhole lead to time travel? You just disappear in one place and appear in some remote place. That's all. There is no any time travel happen. Even if passing through wormhole takes zero time. And why anybody should care how it will look like to some third-party observer? What he could see, whatever weird things it could be, does not change what is really happens.

If we reject relativity, that means we can preserve causality even with FTL…

You still don't get what I'm trying to tell. There is no any casuality problems at all. There is problem of wrong interpretation of observations. Observer could observe some weird stuff, but that does not mean this stuff really happens. If an example with supersonic plane flight when observer clearly hear casuality violation does not make sense for you, I don't know how to explain that in a way you can understand it.

Look, all relativity based on what observer see. But everything I ever read on that topic, silently omit the question about the exact process of that seeing.

When you read something from any other area of science, you see careful (or not very careful, but still) description of how exactly and with what instruments observations was done and how instruments distort observations and how that distortions was cancelled or accounted. F.e. if some voltage is measured, then there is always data for internal resistance and capacitance of voltmeter (or at least its model and you could find this parameters in tech characteristics). Internal resistance of voltmeter could be not a parameter you think about in the first place, but it obviously could noticeably skew observation. So it should be accounted for such observation, and if measured voltage source have internal resistance comparable with internal resistance of voltmeter then observed value should be corrected for voltmeter internal resistance to find real voltage from the observed.

This never done in any relativistic study. They use light to observe something happening with speed comparable with speed of light, but don't correct their observations for that "voltmeter internal resistance", i.e. speed of light that is used to observe. It is just garbage science or fraud, nothing else.

Look, help me understand the implications of this.

Closed time-like curves is a product of general relativity math. That does not mean they are real.

Differential equations could have multiple solutions. Solution of differential equation is a function. So, there could be many functions that fit some theory that uses differential equation, but it could be that only few of them really occur in nature.

In one of my businesses I earn money from practical use of theory with differential equation as its core. (Sorry, I will not disclose exact details, since it could be a way to deanonymise me :) ) To use this theory practically, I have to find solution and use that solution to get result that could be practically verified. It is easy (well, not very easy, but whatever) to get a dozen of solutions, but in practice only few really works and give correct practical results that equal to what I get in practice. All other solutions, being mathematically correct either collapse when things come to real data, either produce complete garbage.

Meanwhile same thing happens with all that "new particle search" thing. Somebody find yet another solution that mean existence of new particle, people spend millions and years to check it, and find out that this solution just don't work in reality, being mathematically correct.

Hopefully, checking solution in my area don't need millions and years, and I don't really interested in producing more solutions, since those I already found works good. May be they are not insanely perfect, and may be there could be better solutions, but customers are fully satisfied, because they just work as intended. They do the job, so no need to search and research new "particles" or "closed timelike curves" for me. Unlike all those theoretical scientists who make money doing that.

Mathematical solution does not mean that it even have some sense. Math is a language for describing nature. And as in any language you could create perfectly grammatically correct sentencies that don't have any sense at all. Same with math.

Adding to that questionability of general relativity in whole, we get something like word salad expressed in non-existing language.

If we reject relativity, that means we can preserve causality even with FTL…

You still don't get what I'm trying to tell. There is no any casuality problems at all. There is problem of wrong interpretation of observations. Observer could observe some weird stuff, but that does not mean this stuff really happens. If an example with supersonic plane flight when observer clearly hear casuality violation does not make sense for you, I don't know how to explain that in a way you can understand it.

Look, all relativity based on what observer see. But everything I ever read on that topic, silently omit the question about the exact process of that seeing.

When you read something from any other area of science, you see careful (or not very careful, but still) description of how exactly and with what instruments observations was done and how instruments distort observations and how that distortions was cancelled or accounted. F.e. if some voltage is measured, then there is always data for internal resistance and capacitance of voltmeter (or at least its model and you could find this parameters in tech characteristics). Internal resistance of voltmeter could be not a parameter you think about in the first place, but it obviously could noticeably skew observation. So it should be accounted for such observation, and if measured voltage source have internal resistance comparable with internal resistance of voltmeter then observed value should be corrected for voltmeter internal resistance to find real voltage from the observed.

This never done in any relativistic study. They use light to observe something happening with speed comparable with speed of light, but don't correct their observations for that "voltmeter internal resistance", i.e. speed of light that is used to observe. It is just garbage science or fraud, nothing else.