A quick thought experiment

  • #1
Suppose in the distant future, converting mass into energy is something as that common and easy as heating food with microwaves are today.

Now, suppose we built one of these energy to mass converters in space and another mass to energy converter here on earth.

Additionally, we connect the two "converters" with a superconducting wire where none of the energy would be loss.

Afterwards, we beam energy from the earth up to the Energy to Mass converter in space where it would create a matter/antimatter pair.

Then we dropped the newly created object onto a kinetic to electrical machine on the surface of the earth.

Next, we would annihilate the object to create energy, converted it to electrical energy, and beamed all the energy back up again and repeated this process again and again.

After doing this process once, we would find that we would gain more energy than we started with due to gravitational potential energy.

Ex.

Input = Matter / Antimatter pair
Output = Matter / Antimatter pair + GPE

So, wouldn't this violate the conservation of energy?
 

Answers and Replies

  • #2
Simon Bridge
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Something very similar to this came up in the Bohr-Einstein letters (iirc).

You are quite correct - the thought experiment as describe violates the law of conservation of energy ... which means you've left something out doesn't it? Can you see the flaw?

Note: there is no difference between mass and "energy", so treat the two words as interchangeable.
 
  • #3
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You are quite correct - the thought experiment as describe violates the law of conservation of energy ... which means you've left something out doesn't it? Can you see the flaw?
Ok let me give it a shot...

Afterwards, we beam energy from the earth up to the Energy to Mass converter in space where it would create a matter/antimatter pair.
This process would account for the added GPE going in the other direction, since you would, in fact, lose energy in this transit. If you are sending "energy" out into space, it is presumably in the form of EM radiation, and the process of sending out of a gravitational well will lengthen its wavelength and therefore lower its energy. Superconducting wires or not it won't make a difference. Is that it?
 
  • #5
Simon Bridge
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@DiracPool: pretty much what I was thinking of, but I had hoped OP would give it a try first ;)
The mistake in the description was to say "energy" without thinking about the form it takes. This hides the "inconvenient" details.

Consider:
If we can convert energy from any form into any other form ... then it must be entirely equivalent to convert some of the mass into kinetic energy in, a matter2KE converter, to throw the remaining mass up to a new height ... let it fall back down, and recover the converted mass in a KE2matter converter. You'll notice that this is the same as converting the matter into gravitational potential energy... any description which makes the equivalence of matter and energy fully into account will appear similarly obvious.
 
  • #6
Khashishi
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Electrical energy has mass. You can't lift electricity for free.
 
  • #7
Simon Bridge
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Electrical energy has mass. You can't lift electricity for free.
... photons don't have mass though - does that mean that you can lift photons for free?

Anyway - in post #1 the electrical energy was used to connect pairs of converters at the same gravitational potential ... an inspecified kind of energy got "beamed up".

Note: this means that the Enterprise has to supply extra energy when beaming Capt Kirk up from a planet surface in order to ensure that all of Kirk winds up on the transporter platform. Probably why the transporter room lights are sometimes seen to get dimmer for a bit.
 
  • #8
So what is the mechanism that reduces the amount of energy available when we "beam" the energy up either via photons or electrons against gravity called?
 
Last edited:
  • #9
russ_watters
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Gravitational red shift.

It means when Captain Kirk gets beamed back up to the enterprise, he arrives with a sunburn.
 
  • #10
BruceW
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... photons don't have mass though - does that mean that you can lift photons for free?
yes they do, 'relativistic mass'. hehe, I'm guessing you are not a fan of this term?
 
  • #11
Simon Bridge
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So what is the mechanism that reduces the amount of energy available when we "beam" the energy up either via photons or electrons against gravity called?
The math covering it, these days, is General Relativity - in that model (and waving hands a lot), the curvature of space-time changes the wavelength observed. There's a QM description too.

You can see that it has to happen right?
Light going from a low to a high altitude gains gravitational PE, so it has to lose kinetic energy.
Since it's light, it cannot just slow down ... but it can lose energy by lengthening it's wavelength.
Hence the effect is called "gravitational redshift" - look it up for more details.

Hand-waving saves me some typing but it don't get you all that far.

@BruceW:
Six of one and a half-dozen of the other ;)
Khashishi may have had another idea though, or may have just been being glib ... hence the question. JIC.

@russ_watters:
Since Kirk gains gravitational PE when beamed up to the Enterprise, doesn't that mean he has to lose energy from someplace ... if he were to lose it from internal energy, wouldn't that make him colder? How would he end up with a sunburn?

Maybe he could lose mass evenly all over ... and when he beams back down, he bulks up ... with the transporter having to do some interpolation ... after lots of away missions he could look a bit blurry with interpolation artifacts and/or pixelation. But I digress.
 
  • #12
russ_watters
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Turning red from the red shift was a joke: redshift is indeed an energy loss. But how it would affect a fictional technology is just more fiction anyway, so if I catch that in the next Star Trek movie, I'm suing.

In seriousness, this is not speculation worthy of pf: this thread should stay more real.
 

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