Infinity in Relativity

[sciman55]

I understand that mass increases to infinity at the speed of light. I also understand that infinite mass needs an infinite force to accelerate in Relativity.

However, if this is true, I do not deny it, but I have something to say about

this and you may find it either wrong, or strange...

 

Starting with classical mechanics (which don't apply to relativistic speeds), It was previously said that zero mass implies infinite acceleration, but is it really true? Let's look again.

 

F=ma

 

Now, say that mass is zero and acceleration is finite (say 5); a zero number times a finite number will, according to mathematic laws, always will equal zero. So,

 

0x5=0 N

 

And using the acceleration formula,

 

a=F/m

 

If force is 5 newtons and mass is zero, again,

 

5/0=0 m/s2

 

Acceleration is directly proportional to force; so, zero mass divided or multiplied by finite forces or accelerations will result in zero N or m/s2, according to mathematics.

 

Now, let's look at the infinite mass.

 

A number multiplied by Infinity (I), is always infinity so,

 

F=ma

 

Let's use 5 again for acceleration and I for infinity. So if any number times infinity equals infinity,

 

Ix5=I N

 

Now let's use again,

 

a=F/M

 

If force is 5 and mass is infinity, infinity divided by any non zero number (like five) is infinity, we get

 

5/I= I m/s2

 

Which leaves me with a conculsion in the form of an essay question. Does infinite mass at light speed really need an infinite force or does it already provide it somehow? Explain.

[Jay-qu]

Some of the things you define are not entirely correct, when dividing by 0 it does not equal 0, try this on your calculator, you get an error, or Undefined.

 

Also you cant accelerate a zero mass particle, it will always go at c

[IDMclean]

my hat is off to you, sir. Jay-qu, you are aware that in some mathematical curcumstances zero is undefined. Like for instance.

 

I the universe exists, and everything that exist is in the universe, then something which is known to exist, which is not present, is undefined. Set theory, I think. Not my best subject (math), but hey.

 

Here's a thought. What if velocity was solely based upon inertia, and that something with higher inertia, than 1 (zero is unacceptable, and undefined result in this case), would have a sub-c velocity.

 

So if Inertia is a ratio of two properties to one another, say electric field to magnetic field, and when it is a 1:1 ratio [math]v = c[/math]. when it is 1:2, 1:3, 1:4 or similar, [math] v = \frac{c^2}{E-B}[/math]...

 

Just some otherwise foolish thoughts.

[Qfwfq]

try this on your calculator, you get an error, or Undefined.

:doh:

The third millenium way to teach math! :)

[sebbysteiny]

If force is 5 and mass is infinity, infinity divided by any non zero number (like five) is infinity, we get

 

5/I= I m/s2

 

Isn't 5/I = 0 thus meaning an object of mass I cannot accelarate?