Physics Greatest Mysteries

[arkain101]

Quote:

Originally Posted by Boerseun

Indeed.

 

A very humbling thought, actually. Consider:

 

If you're able to convert every single atom of all the matter in the observed universe to pure energy (which will be a lot!), you still wont have enough energy to be able to push a single tiny atom past .999999999...999 c. By which stage that one atom will be heavier than all the galaxies, stars and planets combined that you've pulverised to get the energy.

 

Amazing... (still, after all these years!)

 

-----------------------------------------------

 

Thats what really gets me. An atom may travel 99% C in an accelerator but does not increase in mass significantly enough to represent anything close to infinity yet, if it were to go just a bit faster, it will magically transform to more mass than the universe. Where is this fine line that turns .00000000000000000001kg of mass into infinity. seems unlogical.

[CraigD]

An atom may travel 99% C in an accelerator but does not increase in mass significantly enough to represent anything close to infinity yet, if it were to go just a bit faster, it will magically transform to more mass than the universe. Where is this fine line that turns .00000000000000000001kg of mass into infinity. seems unlogical.

There’s no fine line, just a smooth increase in mass as a massive object approaches c. It’s given by the (what should by now seem) familiar equation M=Mrest / (1-(v/c)^2)^.5.

 

Just try the equation using a computer, calculator, or paper and pencil to get something like this

Velocity                            Mass
0                                   1
0.9 c                               2.29
0.99 c                              7.09
0.999 c                            22.37
0.9999 c                           70.71
0.99999 c                         223.61
0.999999 c                        707.11
0.9999999 c                      2236.07
0.99999999 c                     7071.07
0.999999999 c                   22360.68
0.9999999999 c                  70710.68
0.99999999999 c                223606.80
0.999999999999 c               707106.78
0.9999999999999 c             2236067.98
0.99999999999999 c            7071067.81
0.999999999999999 c          22360679.77
0.9999999999999999 c         70710678.12
0.99999999999999999 c       223606797.75

Around here is where your average calculator will start to fail you, but as you can see, there’s no fine line anywhere.

[arkain101]

I see.

 

So how fast does a particle go in an accelerator? .99 or .999999..... ?

[EWright]

There’s no fine line, just a smooth increase in mass as a massive object approaches c. It’s given by the (what should by now seem) familiar equation M=Mrest / (1-(v/c)^2)^.5.

 

Just try the equation using a computer, calculator, or paper and pencil to get something like this

Velocity                            Mass
0                                   1
0.9 c                               2.29
0.99 c                              7.09
0.999 c                            22.37
0.9999 c                           70.71
0.99999 c                         223.61
0.999999 c                        707.11
0.9999999 c                      2236.07
0.99999999 c                     7071.07
0.999999999 c                   22360.68
0.9999999999 c                  70710.68
0.99999999999 c                223606.80
0.999999999999 c               707106.78
0.9999999999999 c             2236067.98
0.99999999999999 c            7071067.81
0.999999999999999 c          22360679.77
0.9999999999999999 c         70710678.12
0.99999999999999999 c       223606797.75

Around here is where your average calculator will start to fail you, but as you can see, there’s no fine line anywhere.

 

Say, I'd like to try to understand this better. Can you point me in the right direction? Where does the origin of the equation and this notion of increased mass stem from exactly?

[cwes99_03]

Hmm, I believe SR. It has to do with the idea of time dilation and light clocks. (personally, I've noted questions about light clocks and the use of added momentum to light by the motion of the emitter on other forums, but I was told I was wrong, so I shrug and go on thinking about these things quietly.)

[CraigD]

So how fast does a particle go in an accelerator? .99 or .999999..... ?

According to this Jefferson Lab link (posted recently by Tormod), they’ve accelerated electrons to .999999992 c, for a mass increase factor of about 7906.

 

Just for fun, I calculated the velocity necessary to increase an electron’s mass (about 10^-30 kg) to roughly equal mine (about 100 kg). It’s 0.9999999999999999999999999999999999999999999999999999999999999999 = 1-10^-65. If you had an accelerator with near 100% efficiency, and used all of the world’s electrical power (about 1.7*10^12 watts), it would take around 70 days to accelerate it to that speed!

[arkain101]

What do they compare the velocity of the atom with?

 

The earth is traveling quite fast around the sun, the sun should be traveling pretty quick aswell around the galaxy, the galaxy should be humming along at a decent velocity aswell.

[CraigD]

Say, I'd like to try to understand this better. Can you point me in the right direction? Where does the origin of the equation and this notion of increased mass stem from exactly?

It stems from the Theory of Relativity. http://en.wikipedia.org/wiki/Theory_of_relativity is a good place to start reading about it, and has links to more detailed wikipedia and other pages, as well as the theory’s author’s original 1916 text (which I think is pretty readable, though several folk disagree with me).

 

An important idea to get up-front when approaching relativity is, although it’s predictions are very important to later theories, it is an extension of classical 17-18th century Physics, containing no “quantum weirdness” or other confusing (but apparently true) features. It’s therefore almost certainly incomplete, yet still very important, and an essential foundation to understanding modern Physics.

[Bo]

What do they compare the velocity of the atom with?

 

with the so called lab-frame, so the frame of reference, where all the detecters and stuff are at rest.

 

the idea of nonconstant physical mass is one of the immediate consequences of special relativity.

 

Bo