Energy paradox? Conservation of energy violated?

[RazzTazz]

TL;DR Summary

Violation of the first law of thermodynamics.

If you have 3 observers, one at rest 0c, one at 0.8c, and one that moves between these 2 frames of reference. The observer that moves between the frames starts at 0c and accelerates all the way up to 0.8c. As it accelerates, the observer in the stationary frame sees its momentum, relativistic mass, KE, time dilation, and length contraction increase. He converts his fuel into KE so he can reach 0.8c. The rocket is in balance since we know by Newton's 3rd law how the rocket gets its KE. The problem arises when you turn from 0.8c back to 0c as you still need to spend energy to decelerate back to 0c. Yesterday people told me that the energy is the fumes and KE that accelerated the rocket, but that is not it because KE is not a physical thing. You accelerate and decelerate back to the original position, but the KE from acceleration was canceled at deceleration so all that is left behind when you reach 0c is just fumes from the rocket, a lot of energy lost, and no work done. You lose your KE energy and that energy didn't dissipate in any sort of radiation or it hasn't done any work. Is like you never left the 0c position if you count just the KE, but you do leave a trail of smoke, head on behind your rocket journey, so for sure you made the trip. SO WHERE IS THE KE? I think I know what's going on with the missing KE, but I want to hear you first. Do you have any answer to this?

 

[Orodruin]

There is no such thing as ”converting fuel into KE” without proper reference to what is actually going on. You need to properly account for conservation of momentum as well as conservation of energy. The rocket can accelerate, but only if it ejects somethig (such as photons) in the opposite direction. If you appropriately account for the energy and momentum of the ejecta, you will not have a problem. Your issue is that you are trying to simply gloss over these details, which typically just ends up in things that make no sense.

 

[Dale]

In general, energy is not conserved in non-inertial frames.

 

[RazzTazz]

There is no such thing as ”converting fuel into KE” without proper reference to what is actually going on. You need to properly account for conservation of momentum as well as conservation of energy. The rocket can accelerate, but only if it ejects somethig (such as photons) in the opposite direction. If you appropriately account for the energy and momentum of the ejecta, you will not have a problem. Your issue is that you are trying to simply gloss over these details, which typically just ends up in things that make no sense.

Ok, so you convert 30% of fuel into gasses, and the rest 70% is used to accelerate your rocket. The trust uses the 70% in both directions by Newton's 3rd law, so you end up with 35% of fuel converted into KE. That is balanced. The problem arises when you accelerate in the opposite direction as KE is not a physical object, it doesn't produce radiation or anything. When you reach 0c, the 35% of KE that accelerated you to 0.8c is canceled by 35% of KE used to decelerate. Your trust already paid for this energy by pushing in the opposite direction when accelerating. But when you reach 0v there is no work done. That energy is like it never existed since it canceled out. So acceleration + deceleration violates the conservation of energy since you need to accelerate for both. Where is the missing energy in the system?

 

[Ibix]

Where is the missing energy in the system?

In the kinetic energy of the exhaust you emitted when you accelerated and the exhaust you emitted when you decelerated.

 

[RazzTazz]

In the kinetic energy of the exhaust you emitted when you accelerated and the exhaust you emitted when you decelerated.

It seems that you don't understand that this is the actual problem. That is conserved, but the KE is not.

 

[Orodruin]

It seems that you don't understand that this is the actual problem. That is conserved, but the KE is not.

Kinetic energy is not a generally conserved quantity.

 

[Ibix]

That is conserved, but the KE is not.

So what? Total energy is the conserved quantity, not kinetic energy.

 

[Orodruin]

Ok, so you convert 30% of fuel into gasses, and the rest 70% is used to accelerate your rocket. The trust uses the 70% in both directions by Newton's 3rd law, so you end up with 35% of fuel converted into KE. That is balanced. The problem arises when you accelerate in the opposite direction as KE is not a physical object, it doesn't produce radiation or anything. When you reach 0c, the 35% of KE that accelerated you to 0.8c is canceled by 35% of KE used to decelerate. Your trust already paid for this energy by pushing in the opposite direction when accelerating. But when you reach 0v there is no work done. That energy is like it never existed since it canceled out. So acceleration + deceleration violates the conservation of energy since you need to accelerate for both. Where is the missing energy in the system?

What you just said makes it explicitly clear that you do not understand the relativistic rocket equation. Please look it up before doing random speculation.

 

[RazzTazz]

Kinetic energy is not a generally conserved quantity.

I thought you referred to KE of the smokes that were released. If KE is not conserved, then we violate the conservation of energy.

 

[Dale]

@RazzTazz you need to do some actual calculations here

If KE is not conserved, then we violate the conservation of energy.

This is false.

 

[Ibix]

I thought you referred to KE of the smokes that were released. If KE is not conserved, then we violate the conservation of energy.

No. You start with chemical or nuclear energy in your fuel. You end up with the same amount of energy as kinetic energy in the exhaust.

 

[RazzTazz]

In general, energy is not conserved in non-inertial frames.

@RazzTazz you need to do some actual calculations here

This is false.

Why is false? What was the KE converted to then?

 

[Orodruin]

I thought you referred to KE of the smokes that were released. If KE is not conserved, then we violate the conservation of energy.

Again: Kinetic energy is not conserved, not even in regular classical mechanics. It is unclear why you think it should be here.

 

[Ibix]

Why is false? What was the KE converted to then?

As already stated, you had energy in your fuel. You converted that to KE if your exhaust and ship during the acceleration, and then into the exhaust during deceleration. The kinetic energy of the two exhaust plumes will equal the energy released by your fuel burning. That is the conservation of energy - your fuel loses chemical energy, your exhaust gains kinetic energy, for a total change of zero.

 

[RazzTazz]

No. You start with chemical or nuclear energy in your fuel. You end up with the same amount of energy as kinetic energy in the exhaust.

Yes, but some is converted to KE for the rocket so it accelerates. The rocket is balanced, but the balance breaks when the rocket starts to accelerate in the opposite direction. Since your trusted paid with KE in the opposite direction to accelerate your rocket, when you decelerate, that payment is in vain, and that is where the problem takes form. The energy is lost in the system.

 

[Dale]

Why is false?

Because the conservation of energy states that total energy is conserved. There is no claim that KE is conserved.

What was the KE converted to then?

That is what you need to calculate. It is your scenario and your claim. You calculate it

 

[jbriggs444]

Why is false? What was the KE converted to then?

Your claim is that kinetic energy is conserved. @Dale objected that this is false.

Consider, for example, a loaded rifle. A cartridge is in the chamber, ready to fire. The rifle and cartridge are at rest. Zero total kinetic energy.

A moment later, the rifle fires. The bullet speeds forward. The rifle recoils. Both have kinetic energy now. The total kinetic energy has increased.

Kinetic energy is not conserved.

To balance the energy books, one can consider the chemical potential energy in the unexploded gunpowder. Total energy (chemical plus kinetic plus whatever else) is conserved. Kinetic energy alone is not.

 

[Ibix]

The rocket is balanced, but the balance breaks when the rocket starts to accelerate in the opposite direction.

This is wrong. Have you computed the energy in the exhaust? If not, you need to do so. If you have, please show your calculations so we can work out where you've gone wrong.

 

[hutchphd]

Ok, so you convert 30% of fuel into gasses, and the rest 70% is used to accelerate your rocket. The trust uses the 70% in both directions by Newton's 3rd law, so you end up with 35% of fuel converted into KE. That is balanced. The problem arises when you accelerate in the opposite direction as KE is not a physical object, it doesn't produce radiation or anything. When you reach 0c, the 35% of KE that accelerated you to 0.8c is canceled by 35% of KE used to decelerate. Your trust already paid for this energy by pushing in the opposite direction when accelerating. But when you reach 0v there is no work done. That energy is like it never existed since it canceled out. So acceleration + deceleration violates the conservation of energy since you need to accelerate for both. Where is the missing energy in the system?

You are using technical words that may sound like physics, but it is assuradly not. This is a well understood system whose solution requires differential equations At no time are "explanations" required and waving ones hands and speaking does not increase that understanding. The solution to the equations of motion is the final word in and of itself..and it conserves all the favorites.

 

[RazzTazz]

As already stated, you had energy in your fuel. You converted that to KE if your exhaust and ship during the acceleration, and then into the exhaust during deceleration. The kinetic energy of the two exhaust plumes will equal the energy released by your fuel burning. That is the conservation of energy - your fuel loses chemical energy, your exhaust gains kinetic energy, for a total change of zero.

Yes, but the KE in both trips cancels out. This is where the problem arises. You use fuel that has mass to convert it to KE and at the end of the trip the mass that you used is not 100% converted to energy because the KE at acceleration and deceleration cancels out, so you end up with 30% 35% less energy in the system.

 

[Orodruin]

The energy is lost in the system.

It is not. You are doing things wrong and just asserting things without doing the actual math. Of course you go wrong doing so!

 

[Orodruin]

Yes, but the KE in both trips cancels out.

It does not. I repeat: do the math! Correctly!

 

[RazzTazz]

It does not. I repeat: do the math! Correctly!

You use fuel that has mass to convert it to KE and at the end of the trip the mass that you used is not 100% converted to energy because the KE at acceleration and deceleration cancels out, so you end up with 30% 35% less energy in the system.

 

[Dale]

the KE in both trips cancels out

Why would KE cancel out? KE is always non-negative. How could one non-negative quantity cancel out another.

Please do the calculations

 

[RazzTazz]

You are using technical words that may sound like physics, but it is assuradly not. This is a well understood system whose solution requires differential equations At no time are "explanations" required and waving ones hands and speaking does not increase that understanding. The solution to the equations of motion is the final word in and of itself..and it conserves all the favorites.

You use fuel that has mass to convert it to KE and at the end of the trip the mass that you used is not 100% converted to energy because the KE at acceleration and deceleration cancels out, so you end up with 30% 35% less energy in the system.

 

[Dale]

@RazzTazz I am pausing the thread to give you time to actually do the calculation of the KE and the total energy for this scenario. Please PM me when you have the calculations ready to post.

Remember the equation for KE: $$KE=\frac{1}{2}mv^2$$This expression should feature prominently in your calculations.

 

[PeterDonis]

As a reference for interested readers, the equations for conservation of energy and momentum for a relativistic rocket (for the case where the exhaust is perfectly collimated photons) are given in this article:

https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

The corresponding Newtonian equations can be obtained by assuming the velocity is much less than ##c##, expanding things out in a power series in ##v / c##, and dropping higher order terms.