Ok, but I would first have to learn to become familiar with such math anyway.
And not just familiar but ensure that it matches the physics without becoming disconnected from reality.
At any rate that would take a while, and would not be super high on my list of things to do.
And to be honest I am not even sure how best to learn to read and work with equations, preferably a free web resource.
Actually I would be genuinely interested in doing that eventually.
BUT how is that going to help this discussion in the present?
That would be when I get around to it and once I become proficient, maybe a year from now best case circumstance unless I become unexpectedly passionate about it.
Maybe I will learn Latin too to be able to tell you all about it in a dead language.
But here and now, if you want the math, then apply it.
If you want to point me to a web resource to take my understanding of math from 2*6+2/3=4.66666 or 5 cubed =125 to the point that I can easily read the equations involved in calculating Relativity or Maxwells equitations then please do.
I’m familiar with what you’re referencing. I know, because I remember doing Muon decay problems in the 4th semester physics class that I took. What I didn’t understand was what you meant by: “distance change to a muon positioned in the center of the rotating muon.”
Futhermore, SR time dilation depends on velocity, not a change in velocity. It’s right there in the formula. Math.
What I meant regarding the Muons was to have one Muon that is an near luminal velocity moving in a circle (orbit), with another muon in our reference frame sitting in the center.
In other words a Bohr hydrogen atom model but with 2 Muons.
Actually you could propose that the center muon is an anti-muon with a positive charge if you like.
The distance is not changing, and the moving muon is not accelerating or decelerating as such.
If you consider the orbit to be acceleration/deceleration, then sure except the G-force could be lowered to 1 G or less with n increased diameter which would put it in the same boat as the center muon, and not possibly responsible for significant time dilation.
To mix things up a bit, set another muon orbiting in the opposite direction and try to calculate all the different expectations, then try to reconcile this with the fact that all frames could be engaged in constant delay communication.
Yes even the counter rotating muons by relaying communication through the center muon.
Now I am going to be told that muons don’t talk to each other.
Why do you consider a particle with 1G (or less) of centripetal acceleration to be comparable to the one in the center with zero centripetal acceleration?
Because he doesn’t want to bother with math, so the fact that 1>0 is quite irrelevant. It’s all right there in his posts… if you had the balls to read them, that is.
Particles such as muons and electrons, bound to a nucleus, do not “move” in an Einsteinian sense. They aren’t actually “orbiting” the way the Moon orbits the Earth. You can’t speak of the electron’s “speed” as it goes “around” the nucleus. That model simply doesn’t work. It was replaced by the quantum model, where the particle is in a bound energy state and has a wave equation describing the probability of its location.
Time dilation is better observed in the creation of unstable particles in the upper atmosphere due to cosmic ray collisions, and the way these particles arrive at the surface of the earth without having decayed. Decay has been delayed because of the tremendous speeds the particles are moving. That is an actual movement, the motion of a particle through space.
Muons in a pseudo-atom – muonic matter – are not actually moving through space.
Because we are in a 1G acceleration field right now, the time dilation is very very slight.
And we have centrifugal motion too, I do not know how many G’s (or what fraction of a G) once you factor in the earth spinning (fraction of a G) plus the earth orbit (no idea!) or the suns orbit around the milkyway (even less of an idea) and when they add up???
Of course I do not consider it to be truly comparable, it is moving at near the speed of light. But I do not consider the centripetal acceleration to change the expectation compared to a linear path, if there is even such a thing as a perfectly linear path in a non-empty universe.
If it did make a difference, then a time difference would be noted the moment the muon deviated from it’s perfect orbital course.
I was trying to explain what I was envisioning since s/he did not understand.
I was not suggesting it becomes an actual atom of muononium.
Indeed there is no significance in it being a muon at all, that was merely what someone suggested. I have avoided particles for the most part to reduce the odds that any talk of wave functions will need to be covered.
Thanks, I and everyone else pretty much knows about the basic concepts of quantum physics, but that is a distraction.
It is worth noting that quantum physics and Relativity do not agree perfectly BTW.
To get some math going in this thread, here’s what I calculate for the radius of a particle moving at .99c with 1g of centripetal acceleration:
a=v[sup]2[/sup]/r
so
r=v[sup]2[/sup]/a
r = [(0.99*299 792 458 m/s)[sup]2[/sup]] / [9.81 m/s[sup]2[/sup]]
r = 8,979,306,327,012,793 m
Does 9 quadrillion meters seem as large a distance to you as it does to me? Because that’s the radius of the orbit the particle would need to have for its cetripetal acceleration to be 1g to ‘‘minimize’’ the time dilation according to you.
To put that distance into perspective, that’s more than 60,000 times the distance between the earth and the sun. And if you recall:
Can you refute what The Hamster King notes about time dialation being a function of distance or show that 9 quadrillion meters is a tiny enough radius of orbit so as not to affect your thought experiment?
While the weight that we experience here on earth is our mass times 1g from f=ma, we do not experience 1g of acceleration if we are not accelerating, do we?
But the particle you propose does experience an effective 1g acceleration away from the center of the 9 quadrillion meter orbit.
So I disagree that the conditions of the two are comparable. But I’m willing to listen where I may have gone wrong so far.
Firstly, I was envisioning a large radius, it doesn’t invalidate it, why would it?
Next, the degree of time dilation expected at .99c is what?
The degree of time dilation expected from a gravity field of 1G is what?
I bet those answers are very very very very very different, which would allow for decreasing the % of the speed of light, and increasing the centrifugal force, and still have the time dilation from the centrifugal force (G-force) still be far far too low to account for the expected time dilation.
That is if time dilation is argued to be caused from such in the first place.
And I am not even sure anyone is, are they?
Additionally I have versions that have no centrifugal force and many other arguments against the centrifugal force either magically making or eliminating time dilation. Read though my previous posts to find some.
If time dilation in the twin paradox was a direct result of G-force from acceleration/deceleration, then the time spent at speed would have no effect on the degree of time difference between the home twin and the travelling twin.
If on the contrary acceleration does not cause time dilation during the acceleration as much as it causes time dilation to occur once at speed when it otherwise wouldn’t have, then a ‘native’ person to a given frame would have a different time rate to someone who had to accelerate to get to that frame! They would be able to meet, notice the difference, and importantly so would an observer that is native to the other frame of motion the traveller left from.
In other words, if the twin in the classic twin paradox found a world that was moving at .99c when she go to that speed, her rate of time would be slower than the natives, and IF not then, then all of a sudden when she comes to a stop, except should would need to age backwards suddenly, yup now we have genuine time travel required! Since she needs to be younger.
OR we could say that the passage of time for the moving twin when they get to that motion isn’t dependant on the acceleration that may or may not be needed to get to or from that frame, since that leads to the most obvious paradoxes.
So then we have time dilation that is occurring because of relative speed and not caring the history of how you came to come into that reference frame.
Time dilation in relativity is broadly speaking the comparison of the “arc lengths” of two different timelike curves. There’s many different factors that can affect the “arc length” of such curves and how we might choose to compare them. Or in other words debating whether time dilation is caused by velocity or acceleration is seriously missing the point.
To the OP: there is so much wrong with what you have said, you’ve made some very elementary mistakes, what you need to do is to pick an elementary textbook of relativity (e.g. one that derives the Lorentz transformation and time dilation/length contraction from first principles). The maths is not that hard.
One thing I would point out though is that the constancy of the speed of light in special relativity in all inertial (i.e. non-accelerated) frames is a postulate of special relativity. That is to say it is a basic assumption (not an argument) and taking this basic assumption we then go on to derive such things as time dilation.
But what mistake can there be in a thought experiment?
There can be a mistake in what the result will be, but I have tried to consider all possible results.
And no one has taken one of my thought experiments (a whole one) and created a non-paradoxical answer, or actually any answer since they have been ignored.
The closest is pointing out that there is acceleration in a rotating path, despite the fact that a limited number of my arguments have curved paths and none of the arguments about why it doesn’t matter that the motion is curved was covered.
Yes, you are right, it is.
But how does that help?
Relativities argument for the speed of light being mysteriously and seemingly impossibly measured to be the same for all frames is because I say so?!?!?!
No explanation for how it is possible, none needed.
Very bold, sure, just not actually possible.
However if almost all objects of any size carry their own aetheric reference frame with them, and if photons tend to move at C relative to an entrained aether frame, and if time dilation and probably length contraction occur when a particle moves through the aether… The result would be sooooooo very close to almost all predictions made by SR. And it has the advantage of not being constantly and unsolvable absurdly paradoxical.
In your train example in your first post the source of your confusion is that you fail to take into account the failure of simultaneity at distance. If there are clocks at two sensors which both display the same time in the frame of observer on the train, they will display different times in the frame of the observer standing by the tracks.
Another mistake you have made, which seems to be one of the main sources of your confusion about special relativity is that the time dilation refers to the rate at which a moving clock is directly observed to run. This is not correct, for example a clock moving towards an observer will appear to run faster due to the Doppler effect, but not as fast as we would expect in the Gallilean case due to time dilation.
Generally speaking in physical theory, such as special relativity, there are right and wrong answers as to the outcome of thought experiments.
I hope by pointing out a couple of elementary mistakes you have made I have rectified that for you.
I have to say I am not sure what you are trying to say here.
It’s an assumption, the validity of that assumption can be tested experimentally (up to a point - the assumption of the constancy of the one-way speed of light can’t be tested, but it is simply easier to assume that the one-way speed is constant if the two-way speed is).
As special relativity has been tested rigorously, it is fair to say it’s assumptions are valid.
Certain classes of ether theories like LET (Lorentz ether theory) are functionally identical to special relativity, but don’t let the fact that you personally find special relativity confusing fool you into thinking they are more useful.
And I’m reminding of this This American Life episode (Act Three) about an electrician who stumbled upon a “revelation that would disprove Einstein”. Equally hilarious things ensue.
