Modern mathematics forbids functions to have more than one y value at a given x value,

Silly modern mathematicians! Don't they remember circles and hyperbolas? Two y coordinates are required for all but two of the x ordinates!

 

True

Actually the mathematics of relativity merely describe what happens to certain physical quantities as velocities approach the speed of light. They provide the equivalent of a discontinuity or pole at the speed of light and no information whatsoever beyond that speed.

There are many phenomenon in Physics where such a discontinuity in the mathematics occurs and the physical phenomenon has (apparently) two values at a particular value. As an example take the transition from sub critical to super critical flow - the 'hydraulic jump' . Modern mathematics forbids functions to have more than one y value at a given x value, but the hydraulic jump indubitably exists and is used to dissapate energy at hydroelectric stations. The mathematics simply can't model the transition area.

Relativity has always constrained itself within certain mathematical boundaries - that is why we have the concept of the singularity. However, one fundamental principles of relativity is that (put crudely) the energy required to move an object of mass at the speed of light is infinite - the preamble of this premise is embedded within the studied laws of physics and mathematics, and I think with regards to this mass travelling FTL, rather than saying there is *other* mathematics, that if it is indeed true; Einstein got it wrong. I have yet to see evidence to convince me this is the case.

Perhaps there is more mathematics than we currently know about beyond light speed?

The Catt anomaly anyone?

http://en.wikipedia.org/wiki/Ivor_Catt

Wow, bizarre views on electromagnetism. Have a look at http://www.ivorcatt.com/2813.htm - this stuff is a discussion all in itself.

Dave

 

I hate to quibble, Dave but a few points.

Firstly it is special relativity that is concerned with the speed of light, not general relativity which is actually a different theory.

Secondly special relativity provides equations which can be solved for any sublight
speed. At light speed they encounter division by zero and are not defined as the mathematicians say. Hence my reference to a pole. We have no knowledge or experience of their applicability or otherwise translight.
I was merely pointing out that in the physical world many phenomena obey different equations at different parts of their range and appear to be able to 'jump' across the discontinuity between the sections of the range.
I have seen no proof positive that this is not also the case with velocity. This opens interesting possibilities.

Remember mathematical equations are only models, not the real thing and don't always work like the real thing or correctly or completely describe it.

A good example would be the commonly taught fallacy of fourier representation of a square wave. As Al Gore would say there is an 'inconvenient truth' called Gibbs Phenomenon which 'requires' infinite response at the verticals of a fourier constructed square wave.

 

I hate to quibble, Dave but a few points.

Feel free to do so; it is a public forum and that is what it is here for.

Firstly it is special relativity that is concerned with the speed of light, not general relativity which is actually a different theory.

Indeed so. My choice not to differentiate between the two types stems from my earlier comment regarding mathematical discontinuities at singularities which are firmly embedded alongside the subject of General Relativity.

Secondly special relativity provides equations which can be solved for any sublight
speed. At light speed they encounter division by zero and are not defined as the mathematicians say. Hence my reference to a pole. We have no knowledge or experience of their applicability or otherwise translight.
I was merely pointing out that in the physical world many phenomena obey different equations at different parts of their range and appear to be able to 'jump' across the discontinuity between the sections of the range.
I have seen no proof positive that this is not also the case with velocity. This opens interesting possibilities.

Remember mathematical equations are only models, not the real thing and don't always work like the real thing or correctly or completely describe it.

I concur. However in the absence of a conclusive set of mathematics for FTL mass movement, then there is a debate to be had. Indeed such mathematics could propose the same inconsistencies that the bridge between General Relativity and Quantum Mechanics has produced. All interesting stuff.

A good example would be the commonly taught fallacy of fourier representation of a square wave. As Al Gore would say there is an 'inconvenient truth' called Gibbs Phenomenon which 'requires' infinite response at the verticals of a fourier constructed square wave.

What one would expect from an infinite series. Sure is an interesting phenonmenon.

Dave

 

Please do if you can, its an interesting topic and one we may not have all the (correct) answers to.

Dave

Hi

I found that information:

http://curious.astro.cornell.edu/question.php?number=167 and that:
http://curious.astro.cornell.edu/question.php?number=575

It does't say that matter travelled FTL though, but that expansion of universe was FTL and that galaxies are moving away from eachother FTL even today.

I've bought a book "Faster Than The Speed of Light: The Story of a Scientific Speculation" by João Magueijo yesterday, who puts a speculation that light once traveled faster in the very early days of universe (Theory of VLS - variable light speed). I'm just waiting for delivery and let you know after the lecture of the book.

Also Dr. Catherine Asaro mentiones FTL Drive and introduces it's working mathematical model. She uses imaginary numbers to think of speed - normally a scalar variable, subject only to increasing and decreasing - as the x-axis of an x-y graph. By adding imaginary numbers - the y-axis - to her speed equations, she can eliminate the relativistic difficulties caused by approaching light speed. Her equations bear a strong resemblance to those used in absorptive dispersion and resonance scattering theory, both of which are closely tied to real-world phenomena. She's still studying her equations to learn if they can yield predictions that can be tested by experimentation.