Transforming Relativistic Kinetic Energy: A Concise Mathematical Trick

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In summary, there was a discussion about a mathematical trick that allows for the rewriting of relativistic kinetic energy as Newtonian kinetic energy multiplied by a function. The function is concise and not a serial development. The question was raised of why one would want to do this and whether it adds any value. The importance of having a peer-reviewed publication or mainstream textbook to support such claims was emphasized. The thread was ultimately locked due to the lack of evidence and the question of whether it was actually useful.
  • #1
quiet
Hi. I have seen a mathematical trick, which allows us to rewrite relativistic kinetic energy as Newtonian kinetic energy, multiplied by a function. The function is concise. It is not a serial development. If anyone is interested I can copy that trick here.
 
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  • #2
Relativistic kinetic energy is ##(\gamma-1)mc^2##. Newtonian kinetic energy is ##mv^2/2##. So the relativistic kinetic energy is ##2 (\gamma-1)c^2/v^2## times the Newtonian kinetic energy. Although this depends on equating Newtonian mass with rest mass, a topic of occasional debate on this forum so there may be a factor of##\gamma## in there somewhere.

The question is why you'd want to do that. It doesn't reveal any interesting physics as far as I can see. It's just algebra for the sake of it.
 
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  • #3
What does one want to do? In my case to have different ways of looking at an issue, that is, to widen the look.
 
  • #4
quiet said:
to widen the look.
What if the other way of looking at it is flawed or doesn't add any value?
 
  • #5
It is true. That can happen. Only You can judge the uselessness of something like that, in case you get to see it.
 
  • #6
quiet said:
It is true. That can happen. Only You can judge the uselessness of something like that, in case you get to see it.
Well, if you do end up posting it, be sure to post a link to a peer-reviewed publication (or mainstream textbook) that also shows it. That it the standard we use at the PF for technical discussions. Thank you.
 
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  • #7
I have not copied the link. Would it be a good idea to remove this thread?
 
  • #8
quiet said:
I have not copied the link. Would it be a good idea to remove this thread?
I locked it, as we usually don't remove threads. But there is still something of information here: As a scientific website, we can ask scientific questions, as "Does anybody know something about the formal connection between ... and ... or is it of any value?" This might - and I'm not saying it does - give rise to an interesting discussion. To state something without any reference or proof is not a scientific method, except it is something more or less obvious. The subject here is more or less obvious, and the question should have been whether it is of any use, and not implicitly assume it is. Also
quiet said:
If anyone is interested I can copy that trick here.
is not a good point to start with. How should your readers know beforehand? And what does "a trick" mean? Tricks normally achieve something, but this is not obvious here and has been rightfully questioned.

Thread closed.
 
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1. How is relativistic kinetic energy different from classical kinetic energy?

Relativistic kinetic energy takes into account the effects of special relativity, such as time dilation and length contraction, on the energy of a moving object. It differs from classical kinetic energy, which only considers the mass and velocity of an object.

2. What is the mathematical formula for calculating relativistic kinetic energy?

The formula for relativistic kinetic energy is E = (γ - 1)mc^2, where E is the energy, m is the mass of the object, c is the speed of light, and γ is the Lorentz factor, which takes into account the effects of relativity.

3. How can I use the "concise mathematical trick" to calculate relativistic kinetic energy?

The concise mathematical trick involves rewriting the formula as E = m(γ - 1)c^2. This allows for a simpler calculation, as the Lorentz factor can be approximated by 1 + (1/2)(v/c)^2 for objects with speeds much less than the speed of light.

4. Can this "trick" be applied to all objects and speeds?

No, this trick is only applicable for objects moving at speeds much less than the speed of light. For objects approaching the speed of light, the full formula for relativistic kinetic energy must be used.

5. How does understanding relativistic kinetic energy benefit scientific research?

Understanding relativistic kinetic energy is crucial for many areas of scientific research, such as particle physics and astrophysics. It allows for a more accurate calculation of the energy of high-speed objects and can help explain various phenomena, such as the behavior of particles in accelerators or the movement of objects in space.

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