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There is one movement action based on two different reference frames.

  1. I’m moving to a fixed wall with velocity $v$ if we take the ground as a reference frame, and I hit the wall and stopped.

The total energy of the system before crash is $E_{\text{ground}} = \frac{m v^2}{2}$, where $m$ is my mass.

The total energy of the system after the crash is $0$, for all the energy is converted to damage in my body and wall, heat, friction, etc.

  1. When we take me as the reference frame, then I have no velocity, but the wall is coming to me with velocity $v$, hits me and stops.

Now,

Total energy of the system before the crash is $E_{\text{me}} = \frac{M v^2}{2}$, where $M$ is the wall's mass.

After: $0$ (Lost in damages, heats, friction, etc)

The question is:

Which physics is true? Which energy is lost? One of them must be true but, I am confused.

Energy and other things change by with the reference frame.

You can tell me why I chose myself as reference frame, it is not correct, I can tell you that we do it often in fluid dynamics, for example jet engines.

Even though air is stationary and jet engines go towards air, we consider that jet engines are stationary, and air comes towards engines, so we do our calculations like this...

Qmechanic
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Jawel7
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  • Does this answer your question? Where does the extra kinetic energy of the rocket come from? – Farcher May 26 '23 at 21:50
  • If you do the calculation assuming that the wall has a large (but finite) mass $M$ and that momentum is conserved, you will find that the mechanical energy loss in both frames is precisely the same, and given by $\Delta E = -\frac{1}{2}\frac{mM}{m+M} v^2$, where $v$ is the initial relative speed between you and the wall. Your mistake - besides jumping between reference frames in the latter scenario - is in assuming that the speed of the wall doesn't change. Its speed doesn't change much, but it loses more energy than you gain and $\Delta E$ ends up being the same. – J. Murray May 26 '23 at 23:37

2 Answers2

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The physics is the same in both reference frames. What changes is what you call "energy". This is a subtle point, so feel free to ask as many questions as needed. I'll try to be as clear as possible.

In the end of the day, our theories are merely theories. They are descriptions of the physical world, but that's all. Descriptions. Hopefully they catch useful information and turn it into more useful information. To be sure we are talking about reality and not only some mambo jumbo, we need to perform experiments.

With this in mind, the question you posed becomes: if I try to measure the energy in this situation you described, which outcome will I get? And the answer is that it depends on how you perform your experiment.

I won't get to details on how to measure the energy, just assume you have an apparatus that can measure the energy of your system of interest. Maybe, to make it simpler, we can consider two balls, $A$ and $B$, colliding and then measuring their energy. Your question becomes to simply consider which energy is correct: that given in the frame of reference of $A$ or $B$?

This depends on how we set up the apparatus. Suppose we set up the energy-measuring-apparatus at rest with respect to $A$. Then this will give the result in $A$'s frame of reference. If we set it up at rest with respect to $B$, we get the result in $B$'s frame of reference. Hence, both energies are correct, but in different frames of reference. Why is this so? Because to get each of the energies, we had to set up different experiments. While we call both quantities "energy of the system", the physical processes required to measure them are different. Hence, they are not the same quantity. We just give them the same name.

The physics does not depend on the reference frame. It is the same regardless of the observer (at least in classical physics) and the reference frame. However, our description does depend on the reference frame. The numbers and such might change, but the damage to your body is the same in both reference frames. We might describe the damage in different manners, but we agree on the damage.

Important Remark

Notice that if you assume the wall gets to rest on your reference frame, then the reference frame in non-inertial and gets sort of weird. If you assume the inertial reference frame that still has the wall moving at a velocity $v$ after the collision, then you actually gain energy due to the force exerted by the wall on you. There's also some energy loss when we consider the wall has a finite mass and will move a little due to the collision. The energy analysis is a bit more complicated than you mentioned (notice, for example, that your computations do not conserve momentum if you assume the wall to have finite mass).

Níckolas Alves
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  • Now, problem begins.. You say “the damage my body takes is the same in both references”, but I don’t think so. I found the lost energy in reference A and B, but they are different in Joules. If the damage I will take is the same, then why quantities are different? If I want to guess what damage I will take before crush, how can I understand? Which frame I will trust? – Jawel7 May 26 '23 at 21:53
  • @Jawel7 This might be merely a miscalculation, too. Check the remark I just added. It could be that the energy variation in this case is the same in both frames. – Níckolas Alves May 26 '23 at 23:00
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    @Jawel7 Do you take the same damage by colliding with a car that you would by colliding with an asteroid going with one thousands times the relative velocity? No, of course not. That's simply an apples and oranges comparison. Energy is a system property. It's not a "single body property". The relative velocity between the colliding bodies identifies the systems and they are simply not the same. The max. amount of energy that colliding bodies can convert to e.g. deformation or heat is given by the sum of their kinetic energies in the center of mass system of the bodies. – FlatterMann May 26 '23 at 23:00
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    @Jawel7 “the damage my body takes is the same in both references” is indeed correct. Lost energy doesn’t cause damage. What causes damage is energy that is converted from other forms into internal energy. That quantity is the same in all frames – Dale May 27 '23 at 02:17
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Energy is relative to the frame of reference, that's how it is. There is certainly an absolute frame of reference, but it does not matter and current physics is not interested in it. It works simply by assuming that all inertial reference frames are equivalent and that the energy depends on the reference frame considered.

externo
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  • Nature doesn't have a need for an absolute frame. That's a human invention and it is almost religious in nature. It also doesn't lead anywhere. If you remove relativity, then you lose the entire framework that makes stable matter possible. What is that good for? You gain a single unnecessary concept at the price of all necessary ones. – FlatterMann May 26 '23 at 22:56
  • Relativity requires a privileged frame of reference. Lorentz's theory proves it. Einstein removed the preferred frame because it was not useful for calculations purposes. But this frame of reference is known to physicists today, it is the CMB frame. Relativity only makes physical sense if you give the univers a frame of reference for the propagation medium and the quantum vacuum. – externo May 26 '23 at 23:16
  • The CMB frame is nothing special. You are merely measuring a relative velocity against a slice of diluted matter that doesn't exist anymore... assuming that the expansion of space along your particular line of sight is the same in all directions, which it wasn't, isn't and never will be. It's a special pleading fallacy, at best. – FlatterMann May 26 '23 at 23:27
  • The CMB frame is similar to that of distant galaxies. The CMB dipole highlights the peculiar velocity of the Earth through space. This peculiar velocity is its velocity relative to the universe. This frame of the universe is the one in which the speed of light is isotropic. If the earth is moving with respect to this frame, the speed of light is no longer isotropic with respect to the earth. It is in this sense that the CMB is an absolute frame : it is relative to it that the speed of light is the same in all directions because it is the reference frame of its propagation medium. – externo May 27 '23 at 00:09
  • One can't measure a velocity against space. One can only measure a velocity against another piece of matter. The speed of light is simply 1 in rational units. That follows directly from relativity. – FlatterMann May 27 '23 at 00:39
  • Yes, we can't. As one cannot Einstein assumed that there was no reference space. But the initial theory, that of Lorentz, said that there was such a frame and that it was hidden. This theory is as functional as that of Einstein and gives a physical cause to relativity. For Einstein, the constancy of the speed of light is the cause of length contraction, for Lorentz it is the opposite: the length contraction is the cause of the constancy of the speed of light. Einstein simply reversed cause and effect. – externo May 27 '23 at 09:28
  • Relativity is explained by the presence of an undetectable medium, and removing this medium amounts to removing the physical foundation of the theory to keep only the equations. In fact, we have today the proof that the version of Lorentz is the good one, it is that the Lorentz transformations are the equations of the classical waves mechanics. These are the transformations undergone by standing waves in motion in their propagation medium. – externo May 27 '23 at 09:31
  • You can check this conversation for more details and some reference links : https://chat.stackexchange.com/transcript/145337/2023/4/13 – externo May 27 '23 at 09:34
  • You need to read this in order to fully understand what I told you about the CMB frame: https://www.researchgate.net/publication/252640513_The_Physical_Interpretation_of_Special_Relativity_-a_Vindication_of_Hendrik_Lorentz/fulltext/563efe5b08ae34e98c4dc003/The-Physical-Interpretation-of-Special-Relativity-a-Vindication-of-Hendrik-Lorentz.pdf – externo May 27 '23 at 12:59
  • Undetectable (aka supernatural) media belong into religion, not science. Science has simply determined that there is no medium and that explains absolutely everything we see. – FlatterMann May 27 '23 at 15:19
  • It is the laws of physics that show that the medium cannot be detected. If you deny the medium you are also denying the laws of physics. You believe that there are magic equations which are called Lorentz transformations and which come from nowhere, this is a religious attitude. Also, you seem unfamiliar with Lorentz's ether theory which is a completely scientific theory and has nothing to do with religion and is the only physical explanation of relativity. – externo May 27 '23 at 15:45
  • This will be my last comment: science is the rational explanation of nature. There is nothing rational about conjuring up unnecessary and undetectable entities. That the human mind has an evolutionary need for objectification is well known. We fell for this fallacy several times over, even in physics. The phlogiston and the aether are two such examples and many people still can't stop the quest for "hidden variables" in quantum mechanics. None of these ideas work. What does work is a simple metric background together with relativity. – FlatterMann May 27 '23 at 15:52
  • The ether theory works perfectly, and John Bell, for example, was its proponent. He wanted it to be taught in universities because it makes relativity intelligible. You are simply confusing physics with mathematics. The fallacy is to believe that the reality is not objective, it is a purely anthropocentric ideology, but on the mathematical plane. Real science is objective. Moreover the Minkowski metric is not the representation of reality, time is a scalar and not a vector dimension and only Hamilton quaternions describe the 4 dimensions of reality. – externo May 27 '23 at 19:46