Why Can't Anything Exceed the Speed of Light?

[jamesfirst]

Why is light the fastest ??

I don't get why nothing can be faster than light.

I know Einstein postulated that speed of light is constant and mass increases and energy increase.

But I am still confused as to why nothing can't exceed speed of light

 

[Pengwuino]

It's not something to "get". You can postulate a maximum speed limit to the world and it happens to be the speed that light travels.

 

[Green Destiny]

I don't get why nothing can be faster than light.

I know Einstein postulated that speed of light is constant and mass increases and energy increase.

But I am still confused as to why nothing can't exceed speed of light

Some current theories already permit the existence of faster than light objects which coincide with our understanding of relativity.

http://www.springerlink.com/content/2316820pux512406/

 

[Kevin_Axion]

Actually, tachyon condensation has rid of those concepts by using String Field Theory, this was motivated by Ashoke Sen. Although tachyons are still being researched within 26-dimensional Bosonic String. If you look at the mathematics of Special Relativity you discover that the speed of light ($$c$$) remains constant in all reference frames no matter how you Lorentz transform (boost - $$(\beta_x,\beta_y,\beta_z)$$) within Minkowski space-time.

 

[jambaugh]

In special relativity space and time are unified into a common space-time. Given this then there is a question of the geometry and units of this new 4-dimensional space-time. The constant c can now be seen as a unit conversion factor between the traditional time units of seconds and the traditional spatial units such as meters. In common units (time in seconds, distance in light-seconds) one then has a speed of light of 1 = 1 light-second per second.

That is just to get the units straight. As to why this is an upper limit to the possible velocities that has to do with the indefinite metric structure of space-time geometry.

Recall that the distance r between to spatial points can be expressed using the distance formula: $$dr^2 = dx^2 + dy^2 + dz^2$$. (where dx, dy, and dz are the differences in x,y, and z coordinate values for the points)
This is the metric structure of space. When it comes to space-time event points we similarly define a metric (in those light-seconds and seconds units) for the proper time between two events. Calling proper time tau writen:$\tau$ we have:
$$d \tau^2 = dt^2 - dr^2$$
where dt is the difference in time coordinates and dr the spatial distance as seen by a given observer. The minus sign is the indefiniteness of the metric.
It is this weird negative which makes the speed limit occur as well as us getting those relativistic effects, time dilation and length contractions.

The proper time tau is the time an object experiences traveling along a straight line through space and time i.e. traveling along a straight spatial line at constant speed. In short you watch me travel from point A to point B which are dr distance apart and your clock shows I take dt seconds to make the trip. My watch shows instead that d tau seconds passed as I experienced it (and I see myself sitting still while first point A and then point B pass me.)

Now the time dilation effect means my d tau will be less in magnitude than your dt. You can even imagine my time is running backwards and this won't matter because we are taking the square of that proper time and so the smallest $$d \tau^2$$ can be is zero.

$$d\tau^2 =0$$ means that $$dt^2 - dr^2 = 0$$ so $$dr = \pm dt$$ and my velocity as you see it is $$dr/dt = \pm 1$$. I'm traveling at 1 light second per second and cannot travel faster without having an "imaginary" proper time which is meaningless (except to say that we suddenly changed the entire geometry of space-time).

As to why space-time has this (hyperbolic) geometry that is just the way it appears to be. It can only be one of 3 cases...

Elliptic geometry: $$d\tau^2 = dt^2 + dr^2$$ in which case we could rotate our space-time velocities all the way around and go backward in time just as we can rotate 180deg in space. We would get time traveler paradoxes left and right. Great for SciFi movies but not so great for reality.

The second case is that we could have a singluar (parabolic) geometry,
$$d\tau^2 = dt^2 + 0 dr^2=dt^2$$
That is what we thought it was before Einstein's theory. But we just were using units where the coefficient of the $$dr^2$$ was very very small but not zero. In second and meter units we get:
$$d\tau^2 = dt^2 - \frac{1}{c^2} dr^2$$
and since 1/c is such a small number in our usual experience we hardly notice it is not zero.

The third case is what we have with hyperbolic pseudo-Euclidean geometry. The speed of light limit comes as the price we must pay to keep the future and past separate.