Done and done both previous posts.
The Relativity of Simultaneity
- Thread starter Motor Daddy
- Start date
Done and done both previous posts.
The answer is two dollars, as you've probably already guessed.
lol, MD knew the answer, he was just testing us
Motor Daddy
Valued Senior Member
Wrong again, it's my perpetual motion machine.
How many times do you need to be told?? NO
Tach said it, I said it, the page you linked to said it. They don't travel at $$2 \times 10^{9}$$ m/s, they travel slower than the speed of light. Seriously, do you know you can scroll down that page? You do realise there's a second paragraph underneath the one you've mentioned? Where it draws a box around 0.989c, the actual speed of the muons?
Why on Earth do you keep asking a question you already have had answered?
Who cares about the speed!?
Important that the same distance the muons reach their destination in less time than photons.
Longer time for the photon. Less time for muons.What is so hard to understand? :shrug:
What's so hard to understand is that's NOT what happens. From the same distance, with the same emission time, photons ALWAYS reach their destination before the muons.
That's what speed is about.
Except they don't. The photons reach first. The initial prediction about the speed of the muons is done in terms of muon count, not in terms of how fast they get from A to B.
If you don't include the fact the muons experience time slower than the Earth you might think they must be moving really quickly for so many to get to the surface before they decay. Faster than light quickly. However, if you were to actually measure their velocity by some means you'd find that isn't the case. The explanation is due to time dilation.
Did you even read the full page you linked to? It explains it all there, what are you struggling to understand?
Two cases:
1) Muons don't reach faster, so there is no length contraction.
2) Muon reach faster, so there carry information faster than photons.
May you know any alternative?
Janus58
Valued Senior Member
Neither of these statement are correct.
There is length contraction of the distance between the base and top of the mountain, in the frame of the muons. But in the frame of the muons, light travels at c relative to the muons. Thus in the frame of the muons, a photon traveling at c leaving the top of the mountain at the same time a muon passes it will head towards the base at c while the base rushes toward the muon at 0.989c. The photon will reach the base when the muon is only ~halfway between base and top.
In the Earth frame, the mountain height is not contracted. The photon and muon both leave the top of the mountain at the same moment. The photon traveling at c and the muon at 0.989c. The photon arrives first.
In no frame does the muon arrive before the photon.
The facts are that the muons live longer than would be expected when viewed from a rest frame due to relativistic time dilation.
I do realise you don't understand this, but then, the universe does not make provisions for your lack of intelligence.
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Janus58
Valued Senior Member
And? The lifetime listed is for the rest frame of the muon. In the rest frame of the Earth (where the distance traveled is 1219 meters) it is ~6.5 times longer. Conversely, in the frame of the muon the distance is ~ 188 meters.
There is no way to conclude from this that a muon crosses the distance in less time than a photon.
Janus58
Valued Senior Member
No, these are the facts according to SR.
Which does not mean what you seem to think it means. It has to be taken in context to the whole explanation on that page. Your idea that this implies that the muon would arrive before light is do to your faulty, and out of context, interpretation of this quote.
The facts are shown above.
Denying the facts due to calculation or theorem is called pseudoscience.
Yes, and you're denying the facts.
In the experiment your link talks about there are at least 2 explanations, either the muons live longer due to time dilation or they move faster than light. If the former is true then in situations where we can measure the speed of the muons directly then we should see time dilation. We can measure the speed of muons in particle accelerators and they live longer.
Muons have never been seen to move faster than light but they have been seen to live longer when they move faster and the relationship between their lifetime and their velocity is precisely as relativity predicts.
The only person engaged in pseudoscience here is you. You're ignoring thing you link to.
Motor Daddy
Valued Senior Member
Huh....
experiment:Muon Velocity
On top of a mountain at 6000 ft a muon detector measures a flux of 550 muons per hour. At a laboratory at the base of the mountain at 2000 ft, a simultaneous experiment measures 422 muons/hr. The half-life of the muon is 1.56 microseconds. How fast were the muons traveling?
Solution: First we will proceed without regard to relativity and the Lorentz transformation.
The distance traveled L=4000 ft x 0.3048 m/ft = 1219 m
The time is then calculated for the two populations as an exponential decay process using the half-life measured in the laboratory.
The results of this calculation are:
distance: 2000 ft , time: 0.596 microseconds , velocity 2.0X10 ^ 9 m / s.
What is there to explain?