# Minimum mass Maximum speed ?

1. Nov 10, 2012

### ChrisPhy

New to this and was thinking about extreme cases to help me get my head around how this all works...need help..

Imagine we have an object with mass moving along. Not that this is possible, but what if all other mass in universe was somehow utilized in some nuclear reaction so ALL energy in universe is used up to accelerate this one object to maximum speed.

Even all the mass in object is used up except for the last smallest atom/sub atomic particle. So we are left with a single particle speeding through space at almost C.

Ok, now at this point how does the particle know that it is not stationary ? And since there is no other stuff out there anymore how is there really and kinetic energy to be recouped ?
At this point isn't the total energy of the whole system down to zero ?

I need help in laymen's terms understanding the progression of total energy in universe during this scenario, and if it is still there at the end, and if so in what form ?

Thanks

2. Nov 10, 2012

### Staff: Mentor

No, you're not. You're also left with a lot of rocket exhaust, or something equivalent. You can't just magically use up the energy in everything else to accelerate one object; the force that accelerates the object has to be applied somehow. There's no way to do that and not have other "stuff" around, and all that other stuff will have energy too. The other stuff will also serve as a reference for determining the relative motion between the one particle you're interested in and everything else.

3. Nov 10, 2012

### tiny-tim

Hi ChrisPhy!
Sorry, but conservation of momentum means that there has to be something going in the opposite direction!

EDIT: ooh, PeterDonis beat me to it!

Last edited: Nov 10, 2012
4. Nov 10, 2012

### Staff: Mentor

We're suppressing conservation of momentum here, I presume? It's still an interesting discussion.
As far as the particle (or an observer moving alongside it) is concerned, it is always stationary, at rest while the universe is moving rapidly backwards relative to the particle. As we proceed through your thought experiment of dismantling the entire rest of the universe and using its energy to further accelerate the particle, in the particle frame there's less and less universe moving ever faster backwards, but the particle is always at rest, and stays that way even as the universe is completely emptied.

And what about the kinetic energy? You've just demonstrated why energy is a frame-dependent quantity - all observers agree that is conserved, but the conserved quantity may be different in different frames. Here's an analogy: If I climb a ladder 2 meters high, all observers will agree that I've changed my height by 2 meters, will agree about how much work went into climbing the ladder, and will agree about how much energy wil be released if I fall back off the ladder again. But one observer (standing on the ground next to the ladder) may say that I started at a height of 0 meters and climbed to a height of 2 meters; while another might say that I started at a height of 100 meters above sea level and climbed to a height of 102 meters. They're both right, and they both agree about the underlying physics - sea level guy is just using a different zero point, so starts with a different value for my potential energy at the base of the ladder.

But back to your empty universe thought experiment... It's worth noting that if the particle is accelerating as opposed to just moving with a constant velocity, in current theories that acceleration will be locally detectable (by an accelerometer, or even just an ordinary bathroom scale) even though there's nothing to say what the acceleration is relative to. A number of respectable thinkers have found this troubling (why should the first derivative of position with respect to time be "less real" than the second derivative?), although the resulting debate tends to be more about philosophy than physics. Try Googling for "Mach's Principle" if you want to go there :uhh:

Last edited: Nov 10, 2012
5. Nov 10, 2012

### ChrisPhy

Thank you everyone for your replies...

I get it, now, .. Thanks for not making jokes about my IQ.