Farsight wrote:lpetrich wrote:Farsight, why do you think that mathematics incapable of giving the reason? What would you consider acceptable reasoning and why?
Because you can't use mathematics to define the terms you use in that mathematics. You have to refer to reality, and the nature of the real world is why c is the limit, not the mathematics.
Farsight, your arguments are based on language, and one can interpret mathematics as a kind of language.
Why don't you read that Wikibooks introduction to special relativity?
SR is based on these premises:
* The laws of nature look the same after linear transformations of space and time, with appropriate transformations of other quantities to match. Newtonian mechanics satisfies this condition, though SR differs from Newtonianism in permitting time to get input from space like space getting input from time.
* The speed of light in a vacuum, c, is a cosmic constant. Anything observed to travel at c will always be observed to travel at c in any coordinate system.
From these two premises, one deduces the form a Lorentz boost.
Newton -- Galilean boost:
t' = t
x' = x - v*t
Einstein -- Lorentz boost:
t' = g*(t - v*x/c
2)
x' = g*(x - v*t)
g = (1 - v
2/c
2)
-1/2
I can quote chapter and verse from Einstein himself on this subject. Farsight, you really have to recognize that your proof-texting Einstein's writings makes you look like a creationist.
Turning to momentum, one imposes conservation of it and applies a Lorentz boost to a glancing collision. One finds relativistic momentum from this:
p = g*m
0*v
m
0 = rest mass
Energy one gets from the work equation dE = (dp/dt).dx = v.dp It is:
E = g*m
0*c
2
Using the relativistic mass m = g*m
0 we get:
p = m*v
E = m*c
2
Yes, Einstein's famous equation.
lpetrich wrote:The mathematics is an important part of the theory, so it is completely legitimate to mention it.
Of course it is. But it's a mistake to think that c is the limit because of the mathematics.
I use mathematics to derive my results, the way that you use hand-waving linguistic descriptions. Your disdain for mathematics is a throwback to Aristotelian physics.
Farsight wrote:lpetrich wrote:The mathematics is completely on-topic. Why do you think it isn't?
Because this is the "Understanding Electromagnetism" thread, and Twiglet is talking about why c is the limit, and then proposed a ballistics exercise. It's just one deliberate dereail after another.
No, it's a VERY simple exercise in putting mathematics to work. Farsight, your main response so far has been "
Why do I need mathematics?"
Farsight wrote:OK Twiglet, I've explained energy and mass, and now I've explained why c is the limit. See
http://www.rationalia.com/forum/viewtop ... =9&t=12686. It's all very simple and it's backed up by the scientific evidence. It ought to tell you
why the various equations of SR apply, with no requirement for any assumptions or laws. And it should fit very tidily with that conceptual model you were talking about.
Can you work out the numbers? Like how momentum and energy increase with velocity.
Light or energy/momentum or action moves at c. Matter is action trapped in a circular path, and for matter to go as fast as light, that action has to be moving linearly at c and still describing a circular path. That means the action would have to be going at more than c, but it can't, because light doesn't travel faster than light.
What makes the light go in circles? How do you get relativistic momentum and energy from that?
Why do I need mathematics?"
