Energy Conservation in Relativity: Perpetual Motion?

[faramund]

TL;DR Summary

Using potential energy and energy-mass conversion to break energy conservation laws and hence power perpetual motion

This is very much, a ... what's wrong with this approach...

Consider a large mass with no atmosphere, i.e. the moon. On it, construct a tower of arbitrary height. On the tower build an energy to mass machine, to convert energy to mass via E=mc^2. Once the mass is created, drop it from the tower, to land on some structure that captures the expended potential energy (wave powered generation via it landing in a liquid/a plate on top of a spring...). On the ground, convert the mass back into energy, and send that energy back up the tower (as either electricity up a wire, or by some kind of direct energy (i.e. laser/radio), ...). The expended potential energy can then be used to pay for inefficiencies in the system, with any excess being the additional bonus energy that can be used for the perpetual motion system.

 

[A.T.]

On the ground, convert the mass back into energy, and send that energy back up the tower (as either electricity up a wire, or by some kind of direct energy (i.e. laser/radio), ...)

When sending it up, you loose all than gain you got when dropping it. No matter how you send it up.

 

[lomidrevo]

electricity up a wire

There are power losses in the wire

laser/radio

Light is redshifted when "climbing" the gravitational potential

 

[faramund]

Well, if its impossible to transfer energy uphill without losses bigger than the gain in potential energy of the equivalent (E=mc^2) mass on the way down, then yup, yet another loony perpetual motion idea bites the dust. How sad ...

 

[Delta2]

Well, if its impossible to transfer energy uphill without losses bigger than the gain in potential energy of the equivalent (E=mc^2) mass on the way down, then yup, yet another loony perpetual motion idea bites the dust. How sad ...

Your thought experiment is interesting, it suggests that whenever we transform mass to energy (e.g electromagnetic energy), then when we send this energy uphill, no matter how exactly we do this uphill transmission, a portion of this energy equal to $\frac{E}{c^2}gh$ is lost (more precisely it is converted back to gravitational potential energy). This also suggest that there must be some interaction between the gravitational field and the field of the other energy form e.g electromagnetic field.

 

[davenn]

Well, if its impossible to transfer energy uphill without losses bigger than the gain in potential energy of the equivalent (E=mc^2) mass on the way down, then yup, yet another loony perpetual motion idea bites the dust. How sad ...

Did you not read the PF rules when you joined ?

PM topics are not allowed, even to discuss why it doesn't work

 

[Ibix]

Did you not read the PF rules when you joined ?

PM topics are not allowed, even to discuss why it doesn't work

To be fair, this one has a good pedigree. It was this experiment that led Einstein to the realisation that there must be gravitational redshift.

 

[faramund]

Well to tell the truth I didn't, but I did do the post, and then the form showed me many related threads on perpetual motion, and so I looked over those to see if I was repeating someone else's concepts, and then discovered that technically I shouldn't of done it.

I understand why there's a non-PM rule, but thinking about why something doesn't work, is always a good way to learn about where one's mental model has weaknesses.

 

[Drakkith]

The rule is there more to prevent low-quality posts by borderline crackpots who want to discuss their ideas by continually cloaking them with phrases like, "why won't this work". Legitimate questions about perpetual motion are usually very easy to answer and can sometimes bring on quality discussions about real physics.

 

[Nugatory]

The title of this thread has been changed (it had been “Perpetual Motion”) because it’s really about conservation of mass/energy in relativity. The thread has also been moved here from the Classical Physics subforum because the classical approximation that mass and energy are separately conserved quantities does not apply here.

 

[martinbn]

Isn't that in essence Bondi's example.

 

[Dale]

Umm, I guess this is no surprise, but thread closed.