If there is a maximum velocity, c, is there a maximum kinetic energy?

[harp AP 2010]

If there is a maximum velocity, c, is there a maximum kinetic energy?

 

[DrGreg]

If there is a maximum velocity, c, is there a maximum kinetic energy?

No, because the relativistic formula for kinetic energy isn't $\tfrac{1}{2}mv^2$ but

$$mc^2 \left( \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1 \right)$$​

which increases without limit as $v \rightarrow c$.

 

[yapabilirsin]

If there is a maximum velocity, c, is there a maximum kinetic energy?

I'm new but I want to say something.
I think that true because DrGreg says similar things.
If we can arrive light velocity, we can see to unproportional increase. I think we will find new formulas for this reason. These formulas can't explain this.

 

[Danger]

Although I am not a scientist, nor even a high-school graduate, I have to voice an objection to DrGreg's response. Bear in mind that this is based solely upon my own internal logic, so I am more than willing to be corrected. My reasoning is that there has to be a limit to kinetic energy simply because the total energy content of the universe is itself finite. Am I missing something?

 

[cjameshuff]

Although I am not a scientist, nor even a high-school graduate, I have to voice an objection to DrGreg's response. Bear in mind that this is based solely upon my own internal logic, so I am more than willing to be corrected. My reasoning is that there has to be a limit to kinetic energy simply because the total energy content of the universe is itself finite. Am I missing something?

The universe itself may very well be infinite. And there's also an argument that the universe's net energy content may be zero, the universe being a fluctuation in local energy levels. The total energy you can bring to bear in any finite time is of course finite, but even if the universe were known to be finite and have a finite energy content, the question was not about how much energy is available in the universe. DrGreg's response was correct. As you approach a relative velocity of c, kinetic energy increases without bound.

 

[cragar]

The universe itself may very well be infinite. And there's also an argument that the universe's net energy content may be zero, the universe being a fluctuation in local energy levels. The total energy you can bring to bear in any finite time is of course finite, but even if the universe were known to be finite and have a finite energy content, the question was not about how much energy is available in the universe. DrGreg's response was correct. As you approach a relative velocity of c, kinetic energy increases without bound.

Sure but like danger said if the energy is finite, you only have so much to fuel it.
But i wonder is it possible that the universe could have an infinite amount of energy.

 

[Danger]

Thanks, Cragar. I don't feel quite so stupid now that someone has agreed with me to some extent.
My understanding is that the universe is considered to be finite but unbounded. Be it the saddle-shape or whatever, you can run around the damned thing forever without encountering a border. Still, though, whatever energy arose from the Big Bang is all that is available for any purpose. I still might be missing something, but that's my take upon the subject.

 

[DrGreg]

Although I am not a scientist, nor even a high-school graduate, I have to voice an objection to DrGreg's response. Bear in mind that this is based solely upon my own internal logic, so I am more than willing to be corrected. My reasoning is that there has to be a limit to kinetic energy simply because the total energy content of the universe is itself finite. Am I missing something?

It's a fair point. My previous reply shows there's no theoretical limit as far as the laws of physics are concerned, but there may well be a practical limit in terms of where you find the energy in the first place.

Having said that, kinetic energy depends on velocity which is a relative concept. It depends on the relative velocity between the object being measured and the observer doing the measurement. So to get a large kinetic energy you could accelerate the observer to a high speed instead of accelerating the object.

 

[cjameshuff]

My understanding is that the universe is considered to be finite but unbounded. Be it the saddle-shape or whatever, you can run around the damned thing forever without encountering a border. Still, though, whatever energy arose from the Big Bang is all that is available for any purpose. I still might be missing something, but that's my take upon the subject.

It's not accepted to be either finite or infinite. There's mathematical models of closed universes, but attempts to measure an overall curvature have failed, meaning the universe is either infinite and flat or so much larger than the portion we can observe that we can't tell. There's no reason to think it isn't infinite, and it's at least a very common assumption that it is in fact infinite and flat.

 

[Danger]

it's at least a very common assumption that it is in fact infinite and flat.

But would it not still be restricted to the original energy output of the Big Bang? If not, where did the extra unlimited energy come from?
DrGreg, thank you for the clarification. I love relativity, but sometimes it warps my brain a bit.

 

[cjameshuff]

But would it not still be restricted to the original energy output of the Big Bang? If not, where did the extra unlimited energy come from?

This question assumes the Big Bang was finite.

 

[Danger]

This question assumes the Big Bang was finite.

How could it not be?
Again, I am honestly asking, not seeking an argument.

 

[rcgldr]

There's a sort of cheat here. The velocity component of energy is relative to some frame of reference, so by choosing a frame of reference that approaches light speed, then all objects kinetic energy relative to that near light speed frame of reference approaches infinity.

 

[cjameshuff]

How could it not be?
Again, I am honestly asking, not seeking an argument.

Why would it have to be?

 

[K^2]

How could it not be?
Again, I am honestly asking, not seeking an argument.

Space-time can in principle have an arbitrary topology. So you can have a situation where universe is infinite, but from any point in the universe it would look like a finite universe expanding from a point.

We see no reason why it would do that, so a finite universe appears to be more likely, but there is absolutely no way, at the moment, to prove it conclusively one way or another, and there might never be.

 

[Danger]

Space-time can in principle have an arbitrary topology. So you can have a situation where universe is infinite, but from any point in the universe it would look like a finite universe expanding from a point.

We see no reason why it would do that, so a finite universe appears to be more likely, but there is absolutely no way, at the moment, to prove it conclusively one way or another, and there might never be.

Ahhh...

 

[cjameshuff]

Space-time can in principle have an arbitrary topology. So you can have a situation where universe is infinite, but from any point in the universe it would look like a finite universe expanding from a point.

We see no reason why it would do that, so a finite universe appears to be more likely, but there is absolutely no way, at the moment, to prove it conclusively one way or another, and there might never be.

It doesn't require any topological contortions...just infinite and flat, the simplest possible topology.

And it doesn't appear to be finite, or to be expanding from any particular point. We can find no evidence of curvature that would let us gauge its size, so it's either infinite or finite but much, much larger than the observable universe. And if it's infinite, there's no reason to think it contains a finite amount of energy.

 

[cragar]

I forgot the scientist that brought up this example but, and this is an approximation,
If the stars in the universe are evenly distributed and there are an infinite numbers of stars , Then why is the night sky dark. Of course there are black holes and other things that absorb light.

 

[cjameshuff]

I forgot the scientist that brought up this example but, and this is an approximation,
If the stars in the universe are evenly distributed and there are an infinite numbers of stars , Then why is the night sky dark. Of course there are black holes and other things that absorb light.

Olbers' paradox. It's not an argument against an infinitely large universe, it's an argument against an large and infinitely old non-expanding universe. We can only see the stars in a finite sphere, increasingly redshifted with distance, against a background of opaque hot plasma red-shifted all the way down to the microwave range.

 

[harp AP 2010]

I would say that there is just a repulsive field force(which requires no energy) moving objects apart(then there would be no definite origin) through a void that goes on forever(flat and infinite).