# Is Kinetic engergy relative to an observer?

## Main Question or Discussion Point

Since all motion is relative to an inertial frame of reference, is a bodies kenetic energy only relevant when the observer is the intertial frame of reference? (i.e. would the kinetic energy be different for another observer and if so does this violate any of the principles of energy conservation or relativity?

This is not for a homework question this is just out of interest.

Me and my physics teacher think this is an interesting topic. Because motion is relative, is speed simply just an illusion created by an observer? If you a traveling at the speed of light in an empty universe (you would be stationary using urself as an inertial frame of reference) so would it be possible to speed up even faster. Since there would be nothing to say your speed is relative to, then speed really is an illusion.

Please answer any of the questions asked or contiue the converstation by adding ideas. Any arguments or criticisms to my statements above are welcome.

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Originally posted by mceddy2001
Since all motion is relative to an inertial frame of reference, is a bodies kenetic energy only relevant when the observer is the intertial frame of reference? (i.e. would the kinetic energy be different for another observer and if so does this violate any of the principles of energy conservation or relativity?
Of course kinetic energy is relative to the observer: it is zero in the body's rest frame, but not zero in frames in which the body is moving. Total energy is also relative.

Me and my physics teacher think this is an interesting topic. Because motion is relative, is speed simply just an illusion created by an observer?
I don't know if I would say that speed is an "illusion", but is a relationship of motion between an observer and the observed body, not some absolute property of the body.

If you a traveling at the speed of light in an empty universe (you would be stationary using urself as an inertial frame of reference) so would it be possible to speed up even faster.
It would violate the laws of relativity for an observer to travel at the speed of light. (Massless objects such as photons aren't really "observers"; their worldlines are not timelike.) The laws of relativity also say that any object that travels at the speed of light is massless, and massless objects can only travel at the speed of light.

LURCH

Originally posted by Ambitwistor

It would violate the laws of relativity for an observer to travel at the speed of light. (Massless objects such as photons aren't really "observers"; their worldlines are not timelike.) The laws of relativity also say that any object that travels at the speed of light is massless, and massless objects can only travel at the speed of light.
But it would also violate relativity for an object that is alone in a universe of its own to be travelling at all. If, as you have mentioned, speed is relative to an observer, and you are the only observer, then no matter what, you're stationary (in any inertial frame).

Originally posted by LURCH
If, as you have mentioned, speed is relative to an observer, and you are the only observer, then no matter what, you're stationary (in any inertial frame).
No, you're moving in any inertial frame, except for your rest frame. It's just all those other inertial frames don't have people at rest in them. It's still meaningful to speak of an object as moving in an inertial reference frame, regardless of whether there is actually anybody at rest in that frame.

since heat is to do with the motion of a particle (vibrations) could heat be relative, would the speed of the earth suddenly changing cause a fluctuation of tempereatures all over the world, or have i just made a question up on complete lack of back ground knowledge?

Relativistic thermodynamics is kind of subtle. Normally you consider a collection of molecules at rest, and the kinetic energy (and thus temperature) depends on the statistical variance of molecular velocity from the average velocity of zero. If you boost to a moving frame, then the average velocity is no longer zero, and the statistical variation is no longer independent of direction: components of velocity change along the direction of the boost, and are unchanged perpendicular to it. In short, I don't know the proper relativistic way of defining the transformation properties of temperature.

Rocksicle
What happens if you have two objects (or observers, or people) moving away from each other at half the speed of light? Does this mean that one object is moving at the speed of light relative to the other? Would either observer be able to see the other?

jcsd
Gold Member
Originally posted by Rocksicle
What happens if you have two objects (or observers, or people) moving away from each other at half the speed of light? Does this mean that one object is moving at the speed of light relative to the other? Would either observer be able to see the other?
No they would not see each other moving at the speed of light, they'd actually see each other moving at 0.8c (v = (u + v')/(1 + uv'/c2).

turin
Homework Helper
Originally posted by mceddy2001
Since all motion is relative to an inertial frame of reference, is a bodies kenetic energy only relevant when the observer is the intertial frame of reference?
While kinetic energy is frame dependent (practically by its very definition), a change in kinetic energy is consistent from one inertial frame to another. Do a calculation for a colission between two massive bodies that is not perfectly elastic. You will find that the loss of kinetic energy is the same in any frame that you perform the calculation (I'm pretty sure of this, but not absolutely positive. I have done the calculation myself for a perfectly inelastic collision, because I had the same concern about kinetic energy).

turin
Homework Helper

Originally posted by LURCH
But it would also violate relativity for an object that is alone in a universe of its own to be travelling at all. If, as you have mentioned, speed is relative to an observer, and you are the only observer, then no matter what, you're stationary (in any inertial frame).
I don't think it violates relativity, but I do agree that motion doesn't make sense in this HIGHLY HYPOTHETICAL situation.