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nLab > Latest Changes: Energy

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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeJun 3rd 2012

    I have created energy ex nihilo. Take that, Hermann von Helmholtz!

    • CommentRowNumber2.
    • CommentAuthorMirco Richter
    • CommentTimeJun 3rd 2012
    • (edited Jun 3rd 2012)

    The energy conservation law doesn’t hold in a relativistic framework. The relation is more involved and the invariant is the energy/momentum/stress tensor.

    Relativistic mass is not the same as the energy. This is only true if the system in consideration has no impulse relative to the observer.

    The rest mass is not the minimum energy in a system but it is the 4-dimension invariant of lets say a field under space time transformation. If you higher the energy by keeping the rest mass constant means you just rotate te energy/impule 4-vector. That way time delay ect come into play. So from the relativistic point of view ’putting’ energy into a system just means a change in perspective between the observer and the system. The total amount of energy/momentum i.e. the length of the energy momentum vector always is constant.

    Everything is traveling with the speed of light always. What we see as actual velocity is ust that the direction of the motion differs from ours

    • CommentRowNumber3.
    • CommentAuthorMirco Richter
    • CommentTimeJun 3rd 2012
    • (edited Jun 3rd 2012)

    In a way Toby, this brings us back to our discussion on the need of bases…

    In the relativistic framework a system ’as is’ has always the speed of light means that momentum and energy is a relativistic concept i.e. depends on the choice of a frame/base. From a ’pure objective’ (everywere)-point of view energy/momentum have no meaning and only the mass (times c 2c^2 if you like) remains.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 3rd 2012

    Toby writes:

    I have created energy ex nihilo. Take that, Hermann von Helmholtz!

    :-) Reminds me of how I recently created antimatter without having created matter yet.

    Mirco boldly asserts:

    Everything is traveling with the speed of light always.

    Yeah, right.

    The energy conservation law doesn’t hold in a relativistic framework.

    First I thought you might be thinking of situations where there is not a time-like Killing vector. But then I realized that you seem to be thinking of Minkowski space, even.

    So I think what the entry needs next is a more solid basis for its assertions by means of some definitions…

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeJun 3rd 2012
    • (edited Jun 3rd 2012)

    In (classical) general relativity the situation is much worse than in special relativity alluded to above. The energy is not even well-defined there. There are some special solutions/symmetries/situations and limits when one can go around this problem but in general it is an unsolved problem.

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeJun 4th 2012

    The energy conservation law doesn’t hold in a relativistic framework.

    I added some remarks about general relativity.

    Relativistic mass is not the same as the energy. This is only true if the system in consideration has no impulse relative to the observer.

    I have not seen this distinction made but it might be good to make it. By “no impulse relative to the observer” you mean that the system’s total momentum (relative to the observer) is constant? If it’s not, then how is the relativistic mass distinguished?

    The rest mass is not the minimum energy in a system

    I just mean that this is the smallest value of energy that any observer will measure. It is the energy inherent in the system, rather than what is observer-dependent.

    Everything is traveling with the speed of light always. What we see as actual velocity is ust that the direction of the motion differs from ours

    In a sense, yes. But this isn’t how physicists usually use “speed” or “velocity”.

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeJun 4th 2012

    I hope that it’s clear that much more remains to be said in this article.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2012
    • (edited Jun 4th 2012)

    Everything is traveling with the speed of light always. What we see as actual velocity is ust that the direction of the motion differs from ours

    In a sense, yes.

    Namely in which sense?

    A lightlike vector has norm 0, a timelike vector has norm different from 0. No Lorentz transformation changes that. I don’t understand what you have in mind.

    There is one way I could make sense of the statement: “Everything is travelling at the speed of light”, but I doubt that this is what you two have in mind. (Namely if we assume the standard-model+Higgs then all fundamental particles are fundamentally massless and you may with some hand-waving at Feynman diagrams read the mass picked up by the interaction with the Higgs as “particles locally zipping around at the speed of light but constantly being scattered off the Higgs such as to effectively move slower”. )

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJun 4th 2012
    • (edited Jun 4th 2012)

    I thought of that second one too, but the way that Mirco wrote ‘the direction of the motion differs from ours’, I took it to mean this idea:

    For timelike or spacelike curves, the natural parametrisation is arclength, and the magnitude of the (mathematical) velocity vector is then (obviously) 11, the speed of light. This parametrisation is unavailable for lightlike curves, but we argue by continuity that the quantity ‘magnitude of the velocity vector with arclength parametrisation’ (which essentially comes out as 0/00/0 in this case) is morally still 11. Since a magnitude of a velocity vector is a speed, and the speed of light is 11 (and it’s easy enough to make it come out explicitly to cc if you want), then everything travels at the speed of light. People will even talk about how an object at rest is moving only in the timelike direction, while a lightlike particle has this speed split between time and space (and an infinite-speed tachyon is moving only in space).

    This idea seems to help some people understand Minkowski spacetime (or maybe it just makes them think that they understand it), but then one has to realise that this is not what a physicist means by “speed”.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2012
    • (edited Jun 4th 2012)

    I see. If that is meant, I’d strongly suggest to speak about it not as “travelling at the speed of light”. As you point out, the argument does not in fact generalize to lightlike motion. The more precise conclusion of this argument is roughly the opposite:

    Everything that is not lightlike is at rest (namely in its own reference frame)! :-)

    • CommentRowNumber11.
    • CommentAuthorMirco Richter
    • CommentTimeJun 4th 2012
    • (edited Jun 4th 2012)
    You can't have a reference coordinate system that itselft has the speed of light. That's one of the basic statement in Relativity. So we only could see light 'from the outside perspective' (perspective is a synonym for base or frame field ect. here) i.e. from a time like base and from there, mass free particles have the speed of light.

    For matter with mass traveling at the speed of light just means that the norm of the energy/momentum 4-vector is always
    $m c$ (or the norm of the four velocity vector $(E/c,v_1,v_2,v_3)$ equals $c$ ). For non quantum fields other than the gravitational one I think (but here I'm not 100% sure) it means that the integral of the potential of the stress/momentum tensor over a (compact) 4-dim submanifold is as well equal to $m c$.

    So if we exclude Tachyons these are all situations.

    @Urs: Saying everything with mass is in rest is not a good picture because: first it favors a reference system. second: What about fields?
    In field theory there are currents ect. that can't be transformed away. Third: A transformation from (for example ) two
    particles with mass into a particle without mass would mean an immediate change of velocity from zero to $c$ i.e. a infinite
    acceleration.

    So especially this last point is only consistent if everything has the speed of light.

    @Toby:

    "Relativistic mass is not the same as the energy. This is only true if the system in consideration has no impulse relative to the observer."

    Sorry there is a translation error from German to English in here: "impulse" should be "momentum"
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2012

    @Urs: Saying everything with mass is in rest is not a good picture because:

    It is at least better than what you had proposed ;-). It’s the way that I could make sense of Toby’s attempt to make sense of what you said.

    But I’d rather see this discussion come back to substantial issues.

    • CommentRowNumber13.
    • CommentAuthorTobyBartels
    • CommentTimeJun 4th 2012

    @ Mirco re relativistic mass.

    I suspect another translation error. The rest mass is the same as the energy if the momentum is zero. But the relativistic mass is the same as the energy regardless. See Wikipedia for terminology.

    • CommentRowNumber14.
    • CommentAuthorMirco Richter
    • CommentTimeJun 4th 2012
    • (edited Jun 4th 2012)
    @Toby: The term 'mass'I used means 'rest mass' it is a scalar invariant of the particle/field. The relativistic mass is only defined relative to a frame. Maybe this is not said often, but physical quantities that changes relative to a frame are (or should be?) called fictitious. That way energy and momentum are fictitious.

    @Urs: No. 'Everything traveling at the speed of light' is the only picture that avoids infinite acceleration at those points where
    (rest)-mass particles are transformed into particles without (rest)-mass. Moreover it is a consequence of the norm value of the 4-velocity vector.

    Maybe I find the time to do a little calculation in a few days for some easy field on Minkowski space to make my point.
    • CommentRowNumber15.
    • CommentAuthorMirco Richter
    • CommentTimeJun 4th 2012
    Maybe I should add: I use the term 'mass' instead of rest-mass because it is an invariant and does not depend on the rest-frame. But as far as I know this is common and not an isolated term I use.
    • CommentRowNumber16.
    • CommentAuthorTobyBartels
    • CommentTimeJun 5th 2012

    I agree that ‘mass’ normally means rest mass in modern physics. Only the phrase ‘relativistic mass’ is different.

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