Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    Offline

    1
    ReputationRep:
    (Original post by shamrock92)
    The fact remains that, since energy is not invariant, and invariant stuff can't be really physical, it can't be physical. Mass is a real, invariant quantity. So energy is just a manifestation of mass, just like magnetic forces are a manifestation of electromagnetism. (More relevantly: it means negative energy isn't so counter-intuitive.)
    Well that's a pretty weird approach to what's physical, it also means that distances, times, momenta, forces and fields aren't physical. Fine if you define physical things to be constrained to be lorentz invariant, you can, I don't agree with that however.

    That also has little to do with negative energy. In no frame can kinetic energy be negative, and when dirac talked about negative energy particles, he was talking about free particles.

    You can also debate whether the mass of a particle changes in SR.
    Offline

    13
    ReputationRep:
    (Original post by TableChair)
    Well that's a pretty weird approach to what's physical, it also means that distances, times, momenta, forces and fields aren't physical. Fine if you define physical things to be constrained to be lorentz invariant, you can, I don't agree with that however.

    That also has little to do with negative energy. In no frame can kinetic energy be negative, and when dirac talked about negative energy particles, he was talking about free particles.
    I'm not saying energy doesn't exist or anything, lol. I just think that it's best understood as a manifestation of mass (because of mass-energy equivalence, and because of energy being non-invariant). That's why the idea of negative energy doesn't scare me that much; it could just be some weird form of inertia.

    (Original post by TableChair)
    You can also debate whether the mass of a particle changes in SR.
    Can you explain that a bit?
    Offline

    2
    ReputationRep:
    (Original post by shamrock92)
    I'm not saying energy doesn't exist or anything, lol. I just think that it's best understood as a manifestation of mass (because of mass-energy equivalence, and because of energy being non-invariant). That's why the idea of negative energy doesn't scare me that much; it could just be some weird form of inertia.



    Can you explain that a bit?
    You say it yourself: mass and energy are equilavent, so whether you think of mass as conserved or energy as conserved is sort of moot

    Energy is conserved if a system is symmetric under time reversal. The total mass in the rest frame is invariant, which is related to the energy-momentum relation

    Oh and in SR then a particle with more energy has more mass (as measured), which is I presume what TC was alluding to. But i'd also presume you knew about this?

    Also, you started off by talking about Dirac and QM, which is based on quantisation of the Hamiltonian - which depends pretty solidly on the 'reality' of energy
    Offline

    14
    ReputationRep:
    Actually quantum field theory depends pretty solidly NOT on the reality of energy- you need to define the vacuum manifold which is the zero point energy and work from that. Chosing a different zero point naturally gives you negative energies. But what I'm wondering is why everyone loves to talk about quantum mechanics and special relativity when the question is a basic one about wave superposition. Maybe it's the fasion in this forum!

    (Original post by TableChair)
    Well that's a pretty weird approach to what's physical, it also means that distances, times, momenta, forces and fields aren't physical. Fine if you define physical things to be constrained to be lorentz invariant, you can, I don't agree with that however.
    No that's wrong. Distances (scalar), forces and fields (tensors) ARE invariant quantities as well. The rest, well, that's observer dependant. Time is certainly real but time measured by one observer is not the same at time measured by another. Same with momenta as it is a result of velocity.
    Offline

    1
    ReputationRep:
    (Original post by john !!)
    No that's wrong. Distances (scalar), forces and fields (tensors) ARE invariant quantities as well. The rest, well, that's observer dependant. Time is certainly real but time measured by one observer is not the same at time measured by another. Same with momenta as it is a result of velocity.
    Distances aren't (also I should have said displacements, but it doesn't actually matter because the norm of a 3-vector isn't Lorentz invariant), at least not in the sense I meant. I could observe an event occurring at the same place but at different times, or in different places but at the same time depending on which frame I was in. Just because it's a scalar does not also mean that it's frame-invariant.

    The definition of a tensor is that it transforms as a tensor, not that it is invariant under transformation. Yes it makes no difference if you transform to another frame, apply the field, then transform back, but they are not Lorentz invariant. If fields and forces were invariant there wouldn't be a magnetic field.

    The only invariant quantities in SR are those obtained by the dot product of two 4-vectors, not the 4-vectors themselves.
    Offline

    14
    ReputationRep:
    You're being inconsistent: you're talking about distance in three dimensions but then go on to say in SR that the only invariant quantities are scalar products of four vectors. Well, distance is the scalar product of two four vectors (two spacetime events). Every single observer can agree on the distance between two events otherwise there would be no meaning to spacelike or time like seperation.

    I think we're tlaking about different transformations.
    Offline

    1
    ReputationRep:
    (Original post by john !!)
    You're being inconsistent: you're talking about distance in three dimensions but then go on to say in SR that the only invariant quantities are scalar products of four vectors. Well, distance is the scalar product of two four vectors (two spacetime events). Every single observer can agree on the distance between two events otherwise there would be no meaning to spacelike or time like seperation.

    I think we're tlaking about different transformations.
    I was referring to three dimensional distances, hence why I further explained what I meant. I thought it apparent since I referred to distance and time separately in my post. Obviously the metric distance is invariant.

    Well I'm talking Lorentz transformations.
    Offline

    2
    ReputationRep:
    (Original post by john !!)
    Actually quantum field theory depends pretty solidly NOT on the reality of energy- you need to define the vacuum manifold which is the zero point energy and work from that. Chosing a different zero point naturally gives you negative energies. But what I'm wondering is why everyone loves to talk about quantum mechanics and special relativity when the question is a basic one about wave superposition. Maybe it's the fasion in this forum!
    Well QFT is still based around Hamilton's principle isn't it - just over all paths, not the just the classical one. So I don't see how energy can be changed from the most fundamental quantity (in classical field theory) to suddenly some 'non-real' quantity. I'm not saying it isn't negative or ambiguous up to some constant and of course it is a somewhat abstract, but it is still a useful quantity in QFT afaik (which isn't actually that much about QFT) which has some physical meaning.

    I think my original point was that energy is just as valid as mass as a 'fundamental' property, so your posts about QFT are just following this 'fashion' that your mentioning.

    I agree the thread shouldn't have digressed so much, but I think that is because Shamrock loves to talk about QM/SR, not everyone, others were just answering his questions.
    Offline

    2
    ReputationRep:
    (Original post by MC REN)
    Energy is conserved if a system is symmetric under time reversal.
    It's time translations, isn't it? Time reversal is different and confusing (it changes the direction of magnetic fields and things).
    Offline

    2
    ReputationRep:
    (Original post by Supermerp)
    It's time translations, isn't it? Time reversal is different and confusing (it changes the direction of magnetic fields and things).
    Yer good point, and of course it is
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 27, 2009
Poll
Do I go to The Streets tomorrow night?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.