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Oh, but your post is: (My boldness.) You said it, not I.

no, you

@mistermack - linked in my first post - The manufacturer has cold weather air source heat pumps in production - https://www.lennox.com/media-room/news/lennox-industries-introduces-new-cold-climate-heat-pump-focused-on-accelerating-environmental-sustainability Alternatives to gas are necessary, for well known reasons; gas is cheaper because the externalities are not counted but those costs don't go away, they are passed on. Disproportionately onto people in warmer climates who didn't burn that much gas.

Neither is mine. And I apologise if any misunderstanding was because of that. There are infinitely many "Lorentz" groups (quite trivially) because the Lorentz group depends on a particular parameter c, the speed of light in the vacuum, that you could assume to take on a different value, and another, and another. Would the new set of transformations it be a group? Of course. Would all the structure generated by the Lorentz group be valid? Of course. You would have time-like, space-like, and light-like vectors, the metric, the whole works. The only exception is provided by the choice c=infinity, with which you recover the Galilean group. But you have to choose what this invariant maximum speed that generates this peculiar geometry (hyperbolically-constrained if you will) is going to be. Other ideas similar to what you suggest have been and are being tried. Namely: doubly-special relativity. And I'm sure the are others still. Doubly-special relativity has different versions. But nothing you say suggests to me that you are trying to go in a similar direction --the interesting one. Rather, you seem to be repeating the known stuff with a different parameter. One such attempt would be totally mathematically consistent. We know, because it was consistent more than a century ago. So the only question is whether it's experimentally true. And we know it to be false.

It's a condition of the paper you cited, so if you're going to rely on that for an example, yes, it's absolutely required. Otherwise the conclusions don't apply to the real world, and it's not valid to use it.

It's a shame you chose to ignore everything that everyone had to say.

I always wonder if Uranus jokes will ever get old. And then I laugh at the next one that appears. So, short answer: No.

In classical mechanics, this would be the case. Physics is more than classical mechanics. EM radiation possesses momentum. This was predicted by Maxwell (i.e. before relativity and QM) and experimentally confirmed in 1903 by Nichols and Hull.

Me neither. As for the other forum I mentioned, I was kicked before I could answer anything. The moderator only said that the post was dumb and that was reason enough. Well, at least some publications out there didn't think the points to be "dumb." The people who are arguing against free will can certainly agree that I "have no choice" in my reactions after being repeatedly treated in such manner. Looks like I "have no choice" but to adopt a hard determinist stance now, since it's so darned convenient! I "have no choice" but to engage in a certain way with academics on LinkedIn, while "having no choice" but "engaging" in an entirely different way on anonymous internet forums. Adopting different views actually have pragmatic effects, but nah, who cares. As long as it's convenient. I "have no choice" anyways.

verb (used without object),ex·plod·ed, ex·plod·ing. to expand with force and noise because of rapid chemical change or decomposition, as gunpowder or nitroglycerine (opposed to implode).

It is interesting that on the one hand beyond the distance of 5 solar radii the light ray should be pradically straight and on the other hand from earth we should consider a displacement of 0.49 for Mercury and a displacement of 1.69 for Neptune, while for the observer on Earth it should be considered that the distance to the sun is similar to "infinite". All this does not make sense. If there is only bending very close to the sun, why should there be a huge difference of the displacement between Mercury and Neptune? And what would be the displacement for all of these planets if the observer was further away than Pluto?

That seems totally unnecessary dude I went through the exercise with the recommended textbook to come up with this solution and put a more detailed answer up here. Idk why you feel the urge to be an asshole about it...

If you cared to read the conversation you were responding to, you would know you don't add anything already said. But if you put it that way, the "general" case does not apply so generally, if there are counterexamples against it. note that the compact space case is just the easiest example to illustrate the issue, so do not make the fallacy to assume its a necessary a condition. oh, sorry it didn't cross my mind that anyone on these forums wouldn't know these, so i didn't understand your question. Yeah, you misread the original post so much, i didn't even bother to try to correct you. But fair enough, especially for physicists, i suppose it is very easy to forget that there is not just one Lorentz group since only the one specific to the speed of light is used in physics. You forgot that if you take the Lorentz group and replace c by any other constant, you get another group with identical structure - and it is also still commonly referred to Loretz group, because in math c play no special role. However, the group acts quite differently on the space, and in particular combining elements of different Lorentz groups end up being elements of neither. So in this case this creates a little ambiguity and i guess i cannot entirely blame someone for stopping reading at "sound wave equation is Lorentz-invariant" and therefore missing out that a different Lorentz group was meant, which should have become clearer when reading further. Since you mentioned the d'Alembert operator, lets go back to the linear acoustic wave equation and notice how we are talking about the same structure - where only the constant is a different one. One could just write \(\Box p=0\) instead but that would omit the material specific propagation constant within, which just fuels the confusion you fell for. But since i apparently do not understand the concepts of relativity, would you please be so kind to enlighten me and the other people in the conversation on the invariances of the d'Alembert operator (or any other operator with the identical structure) and name the 3 subgroups of transformations of the Poincaré group it is invariant under?

I describe an elastic property of space and mention a large number of mathematical consequences. One of these properties is that space and matter are elastically connected and thus that gravity remains a force. - Sir Isaac Newton has given a neat mathematical account of this force. No need to reinvent the deep dish, - in that respect. I also mention deceleration as a consequence. The only equation I have shown is 100% sufficient to mathematically confirm that the equation matches both Pioneer probes deceleration. Anyone can calculate and raise criticism if it is a lie. I mention RR's opposite, (RRT), again the same equation is used. RRT and RR are just 2 sides of the same coin, - and again you see consistency with the speed deviations measured by flyby anomalies. I have shown that mysterious fast speeds in galaxies and clusters (theoretically) can be easily linked with Dark Flow, - again RR can be calculated with the use of same equation, - and furthermore the same equation can be used to calculate Dark Flow Acceleration (DFA is RR's natural equivalent counterpart, in this regard). The interaction and periodic imbalance between DFA and RR will undoubtedly add enormous kinetic energy to orbits of both stars and galaxies. Here there is already a sea of equations suitable for further calculations, and again I must emphasize - there is no need for more. I could go on all night citing examples of the RR equation being sufficient, also when it comes to quasar-inclination anomalies, and so-called planet 9 anomalies, - and a dozen other. Another criticism you mentioned is questions about the background for a modification of THR. The background is that wherever you look, even under your feet, things are moving with due to mysterious forces we cannot account for. One day we will understand that the evidence for what I claim is everywhere, - impossible to overlook. If there is anything specific that you think I have overlooked, please let me know. The equation is universal, - s , - wherever you are.

And you could tell that to Isac New and Einstein also . - One for mass attraction, - One for SR time dilation and one of GR time dilation... and in fact I see nothing, because Einstein borrowed the most important from Lorentz. Goodbuy swanshort.

Like that matters when the only truth is the one people end up accepting “Machines can never be conscious because they work via algorithms” ”nope if they act conscious then they are deserving of rights, and if any human being ends up losing in court against one we’ll punish that rights-violating human” ”but that’s a violation of human rights” ”huh? No idea what you’re crazily rambling about. Now scram” “But the underlying nature of artifacts and algorithms-“ *escorted outside*

Anyone who can separate themselves from personal opinions about the world today and assume a perspective that is all inclusive can see that the world is controlled by the wealthy elite who belong to Zionist groups based in Israel. The USA has become a sword in the hands of the Zionists who hide behind the Jewish culture and exert their will by proxy and believe this keeps their hands clean from the blood that has been spilled in the name of an illegal state spliced on top of Palestine and called Israel. These people state that Israel is the only legal state ever founded because the founding members have law degrees. Most of these peoples degrees were awarded as "Honorary" and it is obvious that these people bent the laws and created new law to meet the needs of their Zionist bosses. They claim antisemitism when they are only one of several Semitic people. Palestinians and Arabs are Semitic and are suffering at the hands of the Zionist groups who are guilty of every charge they accuse others of. Over 2-3 hundred years these people have used resentments and embellished slights of the past to justify and motivate "Jews" all over the world to follow the Talmud, a book written not long ago and meant to be a means of directing Jews to come together in unity against the evil "Goyim", earn money and educate their children as Lawyers, Doctors and Bankers to prepare for the day when they will rule the world. Through manipulative means the wealthiest Zionists in the banking trade have created and implemented a new global economic system that is debt based and controlled by way of The Federal Reserve Banking System that exists in every country with a first world economy. The fed is not owned by the country it is in but is privately owned by the top teer Zionists such as the infamous Rothschilds who became ultra wealthy in the early 19th century. They convinced nations to end the "Gold Standard" banking system that considers a country's tangible wealth when giving loans. With the new system a country can borrow as much as it wants as long as it signs a contract of compound interest and other fees IN PERPETUITY, meaning they pay the debt off FOREVER. This is the motivation behind Feminism. To get as many people working and paying taxes, not to gain equal rights for women. Anyone with a brain can see that throughout the twentieth century things have been manipulated to gain as much power and sympathy as possible so illegal things like the invasion of Palestine would be tolerated. If anyone with a brain and knows basic math were to look at The Holocaust they would instantly notice that gassing and cremating 6 million people in 4-5 years is impossible, even today it takes approximately 40 minutes to cremate one body. Even if it took the same time in the 40's it would take decades to get to 6 million. Do the math yourself and realize that stacking bodies on yop of each other makes the process take longer than one at a time. The Matrix movie is a interpretation of our reality today. We are sources of energy and wealth, nothing more.