'Theory of relativity' and 'The principle of conservation energy' Is it possible to distroy energy ?

[ajanta]

Due to the theory of relativity, clocks tick slower in strong gravity than they do in weak gravity. I have a clock A in strong gravity and another clock B in weak gravity and a 12V DC battery and a 12W filament bulb. Filament resistance of the bulb is 12 ohm. So the Amp will be 1A. Internal resistance of the battery is neglected because it is too low. When the clock A shows 1 second then the clock B shows 2 second. Now I connected the bulb to the battery with long super conductor. If I put the battery in weak gravity that have clock B and put the bulb in strong gravity then what will be ? The battery will discharge 24W energy in two seconds, but how can the bulb will transform 24W electrical energy into heat and light energy within 1second ??

 

[origin]

Due to the theory of relativity, clocks tick slower in strong gravity than they do in weak gravity. I have a clock A in strong gravity and another clock B in weak gravity and a 12V DC battery and a 12W filament bulb. Filament resistance of the bulb is 12 ohm. So the Amp will be 1A. Internal resistance of the battery is neglected because it is too low. When the clock A shows 1 second then the clock B shows 2 second. Now I connected the bulb to the battery with long super conductor. If I put the battery in weak gravity that have clock B and put the bulb in strong gravity then what will be ? The battery will discharge 24W energy in two seconds, but how can the bulb will transform 24W electrical energy into heat and light energy within 1second ??

For someone at the light bulb it will be 2 seconds

 

[Janus58]

Due to the theory of relativity, clocks tick slower in strong gravity than they do in weak gravity.

No, it doesn't say this. It says that a clock in a higher gravitational potential will run faster than a clock at a lower potential. A higher potential in this case means higher in the gravitational field.( a mountain top is at a higher potential than sea level). The difference in potential is related to how much energy is needed to lift a mass from the lower to higher potential. The difference in gravity felt at the two points is not relevant even though higher potential and lower gravity can go hand in hand in the same gravity field.( one example is that Relativity predicts that a clock on the surface of Uranus would run slower than one on the surface of the Earth because Uranus' surface is at a lower potential, however the surface gravity on Uranus is actually less than that of the surface of the Earth.

I have a clock A in strong gravity and another clock B in weak gravity and a 12V DC battery and a 12W filament bulb. Filament resistance of the bulb is 12 ohm. So the Amp will be 1A. Internal resistance of the battery is neglected because it is too low. When the clock A shows 1 second then the clock B shows 2 second. Now I connected the bulb to the battery with long super conductor. If I put the battery in weak gravity that have clock B and put the bulb in strong gravity then what will be ? The battery will discharge 24W energy in two seconds, but how can the bulb will transform 24W electrical energy into heat and light energy within 1second ??

Watts are not energy, they are a measure of power. Energy is measured in watt-seconds(called a joule). 24W for 2 sec equal 48 joules. 48 joules per sec is 48 watts. Thus if Battery B is outputting at 24 watts by his clock, then Light A is receiving at 48 watts. (it burns brighter). So where is this extra energy coming from? It is the gain in potential energy in the electric current as it moves from the high gravity potential to the low potential. (just like a ball gains kinetic energy when dropped from a height.)

 

[krash661]

1Ω = 1V / 1A = 1J · 1s / 1C2

 

[ajanta]

Alien!!!! I'm thinking.

 

[ajanta]

No, it doesn't say this. It says that a clock in a higher gravitational potential will run faster than a clock at a lower potential. A higher potential in this case means higher in the gravitational field.( a mountain top is at a higher potential than sea level). The difference in potential is related to how much energy is needed to lift a mass from the lower to higher potential. The difference in gravity felt at the two points is not relevant even though higher potential and lower gravity can go hand in hand in the same gravity field.( one example is that Relativity predicts that a clock on the surface of Uranus would run slower than one on the surface of the Earth because Uranus' surface is at a lower potential, however the surface gravity on Uranus is actually less than that of the surface of the Earth.

Watts are not energy, they are a measure of power. Energy is measured in watt-seconds(called a joule). 24W for 2 sec equal 48 joules. 48 joules per sec is 48 watts. Thus if Battery B is outputting at 24 watts by his clock, then Light A is receiving at 48 watts. (it burns brighter). So where is this extra energy coming from? It is the gain in potential energy in the electric current as it moves from the high gravity potential to the low potential. (just like a ball gains kinetic energy when dropped from a height.)

No, it doesn't say this. It says that a clock in a higher gravitational potential will run faster than a clock at a lower potential. A higher potential in this case means higher in the gravitational field.( a mountain top is at a higher potential than sea level). The difference in potential is related to how much energy is needed to lift a mass from the lower to higher potential. The difference in gravity felt at the two points is not relevant even though higher potential and lower gravity can go hand in hand in the same gravity field.( one example is that Relativity predicts that a clock on the surface of Uranus would run slower than one on the surface of the Earth because Uranus' surface is at a lower potential, however the surface gravity on Uranus is actually less than that of the surface of the Earth.

Watts are not energy, they are a measure of power. Energy is measured in watt-seconds(called a joule). 24W for 2 sec equal 48 joules. 48 joules per sec is 48 watts. Thus if Battery B is outputting at 24 watts by his clock, then Light A is receiving at 48 watts. (it burns brighter). So where is this extra energy coming from? It is the gain in potential energy in the electric current as it moves from the high gravity potential to the low potential. (just like a ball gains kinetic energy when dropped from a height.)

So we should put our solar panels at higher gravitational potential to collect more energy.

 

[Russ_Watters]

So we should put our solar panels at higher gravitational potential to collect more energy.

No.

 

[danshawen]

krash661 has it right, and the expression demonstrates that energy is conserved.

This is one of the best puzzlers I've seen on a physics discussion forum in a very long time.

Let's restate the problem:

Assume two of the exact same type of clock run by the same type of chemical battery. Place one of the clocks in a gravitational field strong enough so that gravitation time dilation causes time to proceed at 1/2 the rate at which time proceeds in free space, where a second clock and a second battery, both far removed from the gravitational field reside.

Now arrange a power distribution system so that batteries can be swapped (the "free space" battery powering the clock on the surface, the battery on the surface powering the clock in free space). Use superconducting power transmission lines so that energy is not wasted heating the wires. Does this violate conservation of energy?

And a more refined consideration of the same question:

Does it make any difference where you place the ammeter in order to measure the current? Ammeters are placed in series with the load, so you could co-locate the ammeter with the clock on the surface, or you could co-locate the ammeter with the battery in space, at the opposite end of the long superconducting power distribution lines.

The ammeter on the ground with the slower clock will register the same current as it does to power a clock that is running a co-located clock just like it in free space. But the ammeter in free space will indicate that it requires half the current or duty/winding cycle to power a clock that is on the surface at the other end of the long superconducting transmission lines.

This would be the expectation. Another interpretation of electric current is the number of Coulombs of electric charge passing the same point in a current carrying wire. When time slows down, so does current. This checks out also because a chemical battery in orbit would normally discharge more quickly than one on the surface, all else being equal, including loads.

Battery self-discharge rates (shelf life under no load) would also be shorter in free space compared to ones stored on the surface of a gravitating body.

 

[Janus58]

So we should put our solar panels at higher gravitational potential to collect more energy.

No, because light itself gains energy as it goes from a higher to lower potential. Light hitting a higher solar cell will be less energetic than light hitting a lower one. The other thing to keep in mind is in any reasonable gravity field like the Earth's you are not going to see much of a difference. Light falling from some far distance from the Earth will only increase its energy by a factor of ~1.00000000067 as it goes from the starting higher potential to the lower potential of the Earth's surface. ( To get the factor of 2 in your original post you need a much greater potential difference. Your lower clock would have to be no further than twice the Schwarzschild radius away from the center of a black hole.)

 

[ajanta]

When I will put solar panels at higher gravitational potential from lower gravitational potential then it will gain potential energy. So the electrons will gain potential energy. So what will be about the conservation ?

 

[Janus58]

When I will put solar panels at higher gravitational potential from lower gravitational potential then it will gain potential energy. So the electrons will gain potential energy. So what will be about the conservation ?

If you put the panels at a higher gravity potential, the light striking them has less energy then the same light would if you let it continue on to a lower potential and they produce less energy. If you transfer that electricity to a lower potential, it does gain energy, but no more than the light would have traveling across the gravity potential. In other words, if you put the panels on a mountain top and put the load at sea level, the load will not get any more electricity than if you had put the panel at sea level ( less actually when you take transmission loses into account. You can't sidestep or "fool" the conservation of energy.

 

[danshawen]

If solar panels, like batteries, have a shelf life (they do), then they will last longer at lower altitudes. The power distribution is still a CIRCUIT, and as far as that goes, whatever electron goes down must also come back up.

Nothing is gained by an electron going downhill that must go uphill to complete a circuit.

 

[ajanta]

No, it doesn't say this. It says that a clock in a higher gravitational potential will run faster than a clock at a lower potential. A higher potential in this case means higher in the gravitational field.( a mountain top is at a higher potential than sea level). The difference in potential is related to how much energy is needed to lift a mass from the lower to higher potential. The difference in gravity felt at the two points is not relevant even though higher potential and lower gravity can go hand in hand in the same gravity field.( one example is that Relativity predicts that a clock on the surface of Uranus would run slower than one on the surface of the Earth because Uranus' surface is at a lower potential, however the surface gravity on Uranus is actually less than that of the surface of the Earth.

Watts are not energy, they are a measure of power. Energy is measured in watt-seconds(called a joule). 24W for 2 sec equal 48 joules. 48 joules per sec is 48 watts. Thus if Battery B is outputting at 24 watts by his clock, then Light A is receiving at 48 watts. (it burns brighter). So where is this extra energy coming from? It is the gain in potential energy in the electric current as it moves from the high gravity potential to the low potential. (just like a ball gains kinetic energy when dropped from a height.)

Extra energy is transformed into heat and light energy from potential energy. The energy is conserved. But I have to know how it is conserved. The light bulb is connected to the battery with two super conductors. Suppose, they are X and Y. X super conductor is connected to the bulb and to the (-) terminal of the battery,Y super conductor is connected to the bulb and to the (+) terminal of the battery. Electrons are coming down to lower potential through the X conductor and transforming their potential energy into heat and light. So energy is conserved. But electrons are going to the (+) terminal of the battery again through the Y conductor and gaining potential energy. To gaining potential energy again is done by what works ?

 

[exchemist]

Extra energy is transformed into heat and light energy from potential energy. The energy is conserved. But I have to know how it is conserved. The light bulb is connected to the battery with two super conductors. Suppose, they are X and Y. X super conductor is connected to the bulb and to the (-) terminal of the battery,Y super conductor is connected to the bulb and to the (+) terminal of the battery. Electrons are coming down to lower potential through the X conductor and transforming their potential energy into heat and light. So energy is conserved. But electrons are going to the (+) terminal of the battery again through the Y conductor and gaining potential energy. To gaining potential energy again is done by what works ?

No, the electrons reaching the + terminal do NOT gain potential energy.

They react with the electrochemicals in the battery to produce the reaction product of the electrochemical cell. The reaction product is at a lower chemical potential energy than the reactants. That's what powers a battery - a chemical reaction. Once it runs out of reactants, the battery stops working. That happens once all the higher potential electrons have gone round the circuit and gone back into the battery, generating the the lower energy reaction product as they do so.

 

[ajanta]

No, the electrons reaching the + terminal do NOT gain potential energy.

They react with the electrochemicals in the battery to produce the reaction product of the electrochemical cell. The reaction product is at a lower chemical potential energy than the reactants. That's what powers a battery - a chemical reaction. Once it runs out of reactants, the battery stops working. That happens once all the higher potential electrons have gone round the circuit and gone back into the battery, generating the the lower energy reaction product as they do so.

Why the electrons are not gaining potential energy when they are going to the + terminal of the battery from lower potential ?

 

[exchemist]

Why the electrons are not gaining potential energy when they are going to the + terminal of the battery from lower potential ?

Because they are not going "from lower potential". The point of lowest potential in an electric circuit is the battery terminal. For a negatively charged species such as an electron, that is the +ve terminal.

 

[ajanta]

Because they are not going "from lower potential". The point of lowest potential in an electric circuit is the battery terminal. For a negatively charged species such as an electron, that is the +ve terminal.

The + terminal of battery at the lower potential is the terminal of Y super conductor too. But the battery is at higher potential. Will the electrons not gain potential energy when they flow through the Y super conductor to the battery at higher potential ? But why ?

 

[danshawen]

A battery has an internal resistance and so does a load which is a clock, which means that as soon as you connect a superconductor power transmission system to one or both ends, the system no longer behaves as a lossless superconductor. You could use superconducting coils for energy transfer at each end, but as soon as the superconductor powers something, it is no longer lossless in terms of energy.

The rate at which energy is transferred (not the total energy) does depend on any gravitational fields which may be present at either or both ends, as well as any relative states of motion, which is also restricted by tethering it to a power distribution network.

What was the purpose of this thought experiment again?

 

[ajanta]

A battery has an internal resistance and so does a load which is a clock, which means that as soon as you connect a superconductor power transmission system to one or both ends, the system no longer behaves as a lossless superconductor. You could use superconducting coils for energy transfer at each end, but as soon as the superconductor powers something, it is no longer lossless in terms of energy.

The rate at which energy is transferred (not the total energy) does depend on any gravitational fields which may be present at either or both ends, as well as any relative states of motion, which is also restricted by tethering it to a power distribution network.

What was the purpose of this thought experiment again?

Yes its right. I thought about it but my reply is posted before. Because I'm school student and left my study 15 years ago from school. Sorry about it. Would you please explain about it again in simple sentence !

 

[danshawen]

Yes its right. I thought about it but my reply is posted before. Because I'm school student and left my study 15 years ago from school. Sorry about it. Would you please explain about it again in simple sentence !

Time dilation that is due to gravitational effects or relative motion does not violate conservation of energy.

Under certain conditions, certain quantum processes (supposedly) violate conservation of energy temporarily. The rule is, you can borrow a lot of energy for a short time interval, or a small amount of energy for a longer one. Notice that mass and energy are equivalent, so conversion of matter to energy or energy to matter does not violate conservation of energy either, no matter how long or how short a time interval the conversion may require.