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I'm asking apart of the famous twins-paradox of special relativity theory and the ladder-paradox which have been resolved in the literature if there are still some paradoxes or variations of old ones as thought experiments or maybe also some experimental results that today still resist a solution and apparently violate causality?

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  • $\begingroup$ Related: physics.stackexchange.com/q/685215 $\endgroup$ Jan 1, 2022 at 16:18
  • $\begingroup$ A paradox is a teaching tool that tries to get you to understand and learn to avoid unhealthy thinking patterns. It's not an actual scientific problem that ever needed work. $\endgroup$ Jun 20, 2023 at 23:07

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No, there are no unresolved paradoxes in special relativity. It is more than a century old and has been thoroughly studied. At this point in history any claim that there is a logical flaw in SR should be treated with the same or even more skepticism as a claim that there is a logical flaw in the foundations of arithmetic. I use the analogy deliberately: Kurt Goedel, prompted by questions from David Hilbert, did find a "flaw" of sorts in the foundations of arithmetic (the famous incompleteness theorem). Both Goedel and Hilbert studied relativity extensively and did not find any such flaw in relativity.

Not only has it passed logical scrutiny, relativity has passed experimental scrutiny. All of modern physics is based on relativity and quantum mechanics. The global positioning system, modern computers, lasers... they all work as predicted by QM and SR. Atomic clocks are sensitive enough to directly measure gravitational and kinematic time dilation predicted by relativity. Time really is relative, and experiments prove it.

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  • $\begingroup$ The OP asked about paradoxes. There are no paradoxes in arithmetic, for the same reason there are no paradoxes in relativity --- both theories have models, so both theories are consistent. I fear this answer could mislead the OP into thinking there might be paradoxes in relativity that Goedel and Hilbert failed to find. $\endgroup$
    – WillO
    Jan 1, 2022 at 3:05
  • $\begingroup$ @WillO The term "paradox" has a somewhat different usage in physics as opposed to studies on logic. The "twin paradox" is well named. $\endgroup$ Jan 2, 2022 at 12:47
  • $\begingroup$ The mathematics of QM may work well, but I would not say that it is paradox free. The EM wave packet associated with a photon can produce an interference pattern measured in centimeters, but all of its energy and momentum can be absorbed by a single atom. (I have read that there is no evidence that there is a “point like particle” moving with the wave. We can only say that interactions are “quantized”.) $\endgroup$
    – R.W. Bird
    Jan 2, 2022 at 15:54
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Perhaps "paradox" is the wrong word for these. "Example" might have been better.

The universe is approximately classical at low speeds, but we are so used to it that anything else seems to be impossible.

The basis of special relativity is that the speed of light is constant. From this we derive the failure of simultaneity, time dilation, length contraction, and all the other features of SR. These all are how the universe actually behaves (OK, they are a better approximation than classical physics.)

So the paradoxes are just counter intuitive examples of how the universe really works. They were invented as teaching examples.

There are other examples that violate our classical expectations of how things should be. Some of them are not completely explained.

For example, see What is time, does it flow, and if so what defines its direction?. This says that time is very different than you would expect. The common sense view of time is that it flows. The present is all that exists. The future hasn't happened yet. The past is over and gone. But the failure of simultaneity implies the Block Universe is how time really works. A succession of events do not come into existence and disappear. The whole block of events in all of space-time just statically exists. That way I can see a distant event as simultaneous with my "now", and you can see it as simultaneous with my past.

But if time does not flow, why do we see it moving forward? There are still questions about the arrow of time. We accept that time does move forward, do physics with it, and it all works. But it is unsatisfying to classical intuition. And even though asking why the universe works this way has no answer from physics, people still do ask.

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  • $\begingroup$ Causality is the reason responsible for the forward arrow of time. If causality is violated there is no time. Since in this experiment speed is less than c therefore time must exist and so must causality. Meaning despite simultaneity concerns (simultaneity is irrelevant here) and different frames, the two observers must see the same events and in the same order else time, reality and causality have no meaning and should not exist. It does not matter if the two explosions happened at the same point in a spacetime graph, the problem is that the runner dies both outside and inside the barn. $\endgroup$
    – Markoul11
    Jan 1, 2022 at 11:24
  • $\begingroup$ @Markoul11 - What you say sounds reasonable, but be careful about relying on reasonableness. The Block Universe isn't reasonable, and time has other weirdness when you look at quantum mechanics and general relativity. For example, an entangled pair of particles can speed away in opposite directions. Both are in a superposition of spin up and spin down until one is measured. Then the other will always be measured to have the opposite spin. This will happen even if the measurements are so close together in time that the speed of light prevents one from knowing the other has been measured. $\endgroup$
    – mmesser314
    Jan 2, 2022 at 2:23
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Minkowski space is a model for special relativity. A theory with a model cannot be inconsistent.

Moreover, this particular model is so simple (it is basically the study of one particular real quadratic form) that any apparent inconsistency (as opposed to an actual inconsistency, of which there are none) can be resolved quite easily, usually with just a few lines of linear algebra.

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