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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: geordief on 13/09/2016 16:16:51

Title: How can we show that there exists a universal speed limit?
Post by: geordief on 13/09/2016 16:16:51

Suppose we start  with an object in the vicinity of the Earth  and grant ourselves infinite powers to impart energy  to this object in a gradual way  so that it attains a velocity away from us  and the aim is to ascertain the maximum speed  that is possible under these completely unrestricted circumstances.

We have at our disposal the resources of the entire observable universe and an unlimited time to  assemble them for the purposes of propelling the object in any particular direction.

The resources might be assembled in one location  or they might be assembled in some kind of a "repeating, booster" formation . It is unimportant so long as the most efficient method is chosen.

What I want  to satisfy myself is that the "top  velocity speed" between any two points  is in fact a finite  number  despite the possibly infinite amount of resources that can be "thrown at "   the experiment .

What mathematical method or methodology can be use to show this ?

PS To show my bona fides ,hopefully  I am not trying to show that infinite speeds are theoretically possible. I believe ,in fact that there should be a universal speed limit but I am just not quite sure (apart from the geometrical  spacetime arguments I have heard) how it has actually been shown incontrovertibly to be the case.

Title: Re: How can we show that there exists a universal speed limit?
Post by: geordief on 13/09/2016 18:59:26

 I shouldn't reply to myself but is there a mathematical equivalence between using the entire available energetic resources of the universe to impart motion to a massive object and simple using any amount of energy to impart motion to a massless object ?

Also ,as an after thought is it possible to view the speed limit as represented by c  as another way of saying that the speed is actually   infinite (I seem to be contradicting myself in post num.1)?

Can the speed limit be infinite  but still able to be described (because of the geometry of spacetime ) as a finite number?   

Just one last thought. if the universe was finite would that imply a finite speed limit necessarily so that my initial question only arises if it is not known to be finite?                 

Title: Re: How can we show that there exists a universal speed limit?
Post by: evan_au on 13/09/2016 22:28:32

Quote from: geordief

What I want  to satisfy myself is that the "top  velocity speed" between any two points  is in fact a finite  number  despite the possibly infinite amount of resources that can be "thrown at "   the experiment .

Have a look at the Lorentz factor. This describes how the relativistic mass of an object increases as its velocity increases.

You will notice that as the velocity (v) approaches the speed of light (c), the relativistic mass approaches infinity.

So it takes an infinite amount of energy to accelerate a massive particle to a finite speed (c).

This is proven daily in the Large Hadron Collider (LHC), where they accelerate protons to almost the speed of light - but it takes much more energy to get the velocity a little bit closer to the speed of light.

See: https://en.wikipedia.org/wiki/Lorentz_factor#Definition

Title: Re: How can we show that there exists a universal speed limit?
Post by: geordief on 14/09/2016 10:28:24

It seems to me(I am unfamiliar as yet with its use in Maxwell's  equations- I think it may be been discovered even  then?) that the Lorentz factor is verified by experiment but not  "proved" as such.

I am certainly not disputing what has been shown  experimentally to be  the case but I am wondering if there is another approach that could be taken.

Suppose we have a finite system of particles  and  a method of making their relative motions asymmetric ,is there a method whereby  we can quantify the  relative (speed of)  motion between any two particles .

(I realize that "particles" is an approximation of how things are  but can we follow this admittedly flawed logic ?)

So ,is there a mathematical procedure that ,in a finite system of small  objects or particles  would allow one to quantify  relative motion between any two objects  and  ,by extension to  find a maximum value as a function of the overall number perhaps of the objects?

If this was a theoretical /mathematical possibility then it would satisfy my (mathematical?) curiosity to increase to number of particles without limit and determine  what this number would be as it would be another way of evaluating the "maximum speed limit"

Don't get me wrong . If "my" figure differed from c ,I would agree it was probably (very probably ,even certainly) wrong but this is an avenue I am trying to go down but am limited by my lack of mathematical skills.   

Title: Re: How can we show that there exists a universal speed limit?
Post by: evan_au on 14/09/2016 23:18:19

Quote from: geordief

I think it may be been discovered even  then?) that the Lorentz factor is verified by experiment but not  "proved" as such.

It was proven mathematically by Einstein in the Special theory of Relativity.
It has been verified many times since.

Quote

So ,is there a mathematical procedure that ,in a finite system of small  objects or particles  would allow one to quantify  relative motion between any two objects?

If you had a gas of extremely hot particles, you could find one heading to the right at close to c, and another one heading to the left at close to c.

You may think that the speed of one particle as viewed from another would be close to 2c.
But velocities close to c do not add up in the way you expect from your experiences at low speeds. In fact, they can't exceed c.
See: https://en.wikipedia.org/wiki/Velocity-addition_formula