Since you’re proposing this, you should be able to give us answers to questions.
Where does the energy come from to push the muon to 2c or 10c? Exactly how much energy is required to do this? Is the extra amount of energy needed to go from 2c to 10c linear or exponential or something else? Provide the equation. Also, give the experimental apparatus needed to measure the muon at faster than light speed. Can information be transferred at faster than light speed? How can this be shown experimentally? Does faster than light speed violate any conservation of energy laws? If so, in what ways? If not, why not?
I invite others to add additional questions that this proposal generates.
Neither A nor B is a number. They are clocks travelling in space. So how do you come up with a comparison operator for a objects travelling in space? Even in a Galilean universe l would be expecting to designate the object with minimally position and velocity, even of we ignore rotation. So at least a six-vector. You need to define how you are comparing these vectors.
Currently it appears that you are using A and B as shorthand for something, but not being forthright about what.
I’ll give you a hint. You are misusing the notation, and using A and B twice with different meaning each time. That is just a slight of hand attempt to claim a contradiction where none exists. That you have failed to define what A and B mean, and just slide from an object travelling in space to a numerical comparison is just plain faulty logic. I can prove anything I wish using such a tactic. It is a waste of time. What you mean is:
B_A < B_B \wedge A_B < A_A
Where the subscript denotes apparent rate of clock as viewed from.
There is no contradiction here.
Every time you do this you are sliding back into a Galilean universe, and you don’t even realise it. It remains a simple problem. You don’t believe in relativity, so much so that you don’t even realise when you are implicitly casting your arguments in a Galilean view. This nullifies the argument. It becomes just meaningless text and symbols.
Relativity provides the required mathematical definitions, and does so without contradiction.
Touche! I could’t find a reference to speeds in particle accelerators, so went for one I could find. The Frisch (sorry I mis-spelt it) & Smith experiment is here :- https://www.youtube.com/watch?v=tbsdrHlLfVQ .
Another analogy that won’t help: all economic activity is premised on the fact that people value things differently. When I’m hungry, the value I assign to the money I have on hand (Am) is less than the value I assign to the steak (As) I’d like to eat - but the value that the restaurant assigns to the money (Rm) is greater than the value that the the restaurant assigns to the steak (Rs). As>Am and Rs<Rm. You could decide that these are “subjective” values - but they prompt real action - I’m willing to give my money to the restaurant and they are willing to give me the steak. Should we just shout “contradiction” in dismay, instead?
No it does not mean that. I expect you to use Lorentz’s formula, which was designed to answer such questions. Further, I expect you to to look at clock B from clock A and give the result, and look at clock A from clock B and give the result. Bear in mind that Einstein said that these effects are real.
I am being specific. I spelt it out recently. Use the Lorentz equations and note the reading of clock B from clock A, then note the reading of clock A from clock B. This is supposed to be a real effect, not an appearance. Clock A will be ahead of clock B, and clock B will be ahead of clock A. This mathematically is A > B and B > A, which takes no great genius to see is impossible.
There is a way to break the light speed barrier; and one that probably occurs on a regular basis with charged particles. Consider these different arrangements of electrons:
Imagine two electrons held close together. There is a large opposing force between them and they would quickly fly apart if let go. As they move apart, the force between them decreases. Classical mechanics tells us that the force between them will always be greater than zero, no matter how far apart they are, and therefore the electrons should move toward an infinite speed. But SR will say that their mass will increase and keep speeds less than light. So at this point FTL has not been achieved and we move to the next example…
Now imagine five electrons held in a straight line with equal spacing. When they are released, the middle electron will remain motionless; but this time the situation for the other electrons is different. If the middle electron is number 0, then SR tells us that electron 1 must eventually accelerate to near light speed relative to 0. Likewise electron 2 must accelerate to near light speed relative to 1. So electron 2 is now travelling at nearly double light speed relative to its starting point.
Every electron feels a force from all the others, but due to the distances, the primary force will be from the nearest electrons. SR has not been violated because no electron is moving at FTL from its neighbour.
I most certainly am bantering semantics. Your semantics are ill formed.
How do I compare two clocks? Define terms exactly. Be clear about reference frames.
That does not answer any of the questions I asked you. You keep avoiding any questions about real-world experiments as well as avoiding working out formulas to provide predictions for experimenters to test. That is not science. I asked specific questions which should be easily answerable given your assumptions. Please answer them.
This is false. You’re using Newtonian concepts that have been shown to be a good approximation at low speeds but are wrong at high speeds.
And, on the subject of clocks, if you’re in spaceship A and measure B’s clock as slower, and B does the same, as someone asks above, how do you plan on comparing them to see the “true” answer? Does B turnaround and come back? Does A? From A, any experiment A does will show that B’s clock is slower, and vice versa. Now, you want to get the clocks next to each other to show the “contradiction” – how will you do that?
So, you are not actually asking what is observed, only what the math says?
The math has been done, and shows what it shows, that in reference frame A, clock B ticks slower than clock A, and that in reference frame B, clock A ticks slower than clock B.
In order for there to be a contradiction, you would have to actually be in a position to observe that contradiction. There is no place you can be where you would observe this contradiction.
The observation that could be made is that the person riding with clock A sends a signal to the person with clock B, and says, “I see that your clock is ticking slower than my clock.” Then the person at B replies, “And I see your clock is ticking slower than my clock.”
Wait. this Frisch and Smith paper from…1963?! 60 years ago? Ah well…
“Thus, not only does our experiment give direct qualitative evidence of time dilation, but the observed numbers support the quantitative prediction of the Special Theory of Relativity”
A and B are apples, on a table, with two people observing them from opposing directions. How is it possible for the two people to disagree about which apple is in front of the other? How does geometry permit this contradiction?