[puppypower (OP)]

Say we added a fixed amount energy to stationary object. It achieves a final known velocity. All  relative frames of references, to that original frame, will not be valid when doing an energy balance. Relative velocity may work for velocity, but energy is not relative, since it is part of a universal energy balance.

For example, we have a train that burned X gallons of fuel, to achieve a final velocity of 50mph. It drives past a train station, where a sitting man assumes all frames are relative. He assumes he is moving and the train is stationary. Will both calculate the known energy balance; actual fueled used, based on their own frame?

The answer is the man at the station will calculate too little energy, since his mass and his assumed relative velocity, inputted into 1/2MV2 will be way too low. He will violated energy conservation. The train will calculate the correct amount. Relative frames have a narrow limit of application. It works better if we avoid any energy balance. An energy illusion can appear from velocity.

Say the man continues to believe he was the preferred frame; easiest for him to use, due to the assumption of relative frames. We tell him the answer to the energy balance was X amount of fuel. His calculation says much less than that. But since all frames are relative he tries to explain the difference as being due to the extra energy having been transformed into something else that is still being conserved. It is out here, but not easy to see; He may call it shadow energy and say it is another dimension. He will never see this in the lab, since this is not real, but it is needed due to misuse of relative frames in the light of energy conservation.

[Kryptid]

energy is not relative

Yes, it is.

where a sitting man assumes all frames are relative

He isn't merely assuming that.

The answer is the man at the station will calculate too little energy, since his mass and his assumed relative velocity, inputted into 1/2MV2 will be way too low.

No, he won't. You are simplifying the situation too much if you think each viewer will calculate a different number of gallons of fuel used. In each frame, the relative speed of the rails and of the air itself will have to be taken into account as well. Each observer will calculate the same drag and friction and thus get the right answer about the amount of fuel burned.

He will violated energy conservation.

No, he won't. Energy is frame-relative.

But since all frames are relative he tries to explain the difference as being due to the extra energy having been transformed into something else that is still being conserved. It is out here, but not easy to see; He may call it shadow energy and say it is another dimension. He will never see this in the lab, since this is not real, but it is needed due to misuse of relative frames in the light of energy conservation.

No, that is not how relativity works. Energy doesn't have to be turned into "something else".

@puppypower I have seen you post this same misunderstanding about relativity over and over again and you have been corrected about it over and over again to seemingly no avail. Energy is frame-dependent. I'm going to have to ask you to stop doing this as it is becoming tantamount to spam.

[puppypower (OP)]

No, he won't. You are simplifying the situation too much if you think each viewer will calculate a different number of gallons of fuel used. In each frame, the relative speed of the rails and of the air itself will have to be taken into account as well. Each observer will calculate the same drag and friction and thus get the right answer about the amount of fuel burned.

The fuel used by the train is a fixed known amount. This energy value is the energy balance in that scenario and does not need any mental acrobatics to calculate.That value of the fuel consumption and its energy value, takes into account everything; including friction, leading to the final velocity. Nothing is 100% efficient, so there will also be an entropy gain, with this energy no longer being net useable by the universe, so the 2nd law is not violated.

The man on the train assumes a relative velocity to to the frame connected to the entropy and energy balance. If he did not know the fuel answer in advance, he would not know where to stop his analysis to make it all appear to add up.

If he was fully objective he may wonder how the atmosphere of the earth, is moving at the same speed and direction as him, when the weather man says today is a quiet wind day. However, he appears to sees 50Mph wind yet none of the trees are swaying although in linear motion. He may also see that the mountain range in the distance is also moving with him. Those mountains have way more mass than the train. The energy needed would be huge.

If the stationary man was rational, he would realize all these things moving with him makes little sense compared to only a train moving. His calculation would also be way more than the fuel any train can hold. He was living in a relative fantasy world, where mountains and forest move when he decides he is in motion. He could get a reality check by simply by knowing the reality fuel consumption. The train on the other hand, is more self contained since it received the fuel that is making this all happen. It is not a good reference to trip out on.

When Einstein said reference is relative, he was talking about relative velocity, in situations where we cannot know the true energy balance. Two space ships in space with no way to reference to an absolute point in space, time or energy, will cause us both to see relative velocity. This was not so much a fact of life, but an experimental artifact that we get when we do not know the correct energy balance; such as in deep space or in ego centric day dreams at train stations.

If the man at the station knew the fuel consumption energy value constant in advance, he could cherry pick which parts of his relative universe he wished to include in his relative velocity to make it add up correctly. He would not choose the mountain range that appears to be moving since this will mess things up. On the other hand, if he does not know the fuel, and he was very thorough, he will take the energy balance way too far; everything in sight, and add extra energy to the universe that was never there.

Dark energy and Dark matter have never been seen in the lab to know if they are real. These appears to be connected to the relative reference assumption taken was too far.  It adds energy that it assumes is there, but may not be. The analogy is me seeing something like deer tracks in the woods and then assuming this proves unicorns. Unicorn have never been seen in the lab so we would question this. Show us the unicorns and dark energy in the lab since we have tracks in the woods and universe respectively.

Say we got rid of the mountains moving; need for dark energy unicorns never seen in the lab. The energy balance is smaller so we need to another explanation, that uses less energy. If we combine the equivalency principle, we have the exothermic output of gravity as mass lowers  gravitational potential. This will create an affect that look like anti-gravity such as centrifugal force; rotation, and expansions. There is no extra energy needed; correct fuel amount.

[Kryptid]

Puppypower, anyone in any reference frame can correctly calculate the amount of fuel that the train uses. If I had a train on a treadmill inside of a wind tunnel, I could easily arrange for the train to be in the same reference frame as myself (not moving relative to the ground) yet the train will still be expending fuel because the wind and rail friction will be trying to push it backwards.

There is no preferred reference frame. Period. Energy is relative to reference frames. Period. A person onboard the train can easily model themself as sitting still while mountains are moving past them. There is nothing wrong with that. Even in that reference frame, the calculated fuel consumption of the train will be the same.