I'm trying to understand the ^2 in E=mc^2, which I worked back to d = (1/2)vt. So, looking at the area of the graph I understand why 1/2, but then I started thinking, v is simple distance over time, so how could distance - 1/2 distance
Supposing I was asking this before Newton invented calculus...
Is it really d_1 & d_2? I'm just trying to get a handle on what the real world representations are rather than symbol manipulation
@JohnRennie My understanding of the ^2 in Einstein's equation is that all things are already moving at c (speed of causality) through time and we are squaring it because of relative velocity, right?
The problem is that if I starting throwing terms like energy-momentum four vector it's going to sound like voodoo.
It isn't of course, it's just that all disciplines have their specialised terminology and it sounds like black magic unless you're familiar with the area.
This applies to bricklaying or ironmongery as much as it does to physics!
Okay, then, instead of trying to show me the derivation, why not just say what the symbols mean? It'a all aymbolic logic, but the symbols stand in for real world phenomena. So, in the E=mc^2 equation, E is energy, the ability to do work, yes?
@RubelliteYakṣī well yes it is. If you travel for a time t at a velocity v then the distance travelled is s = vt. In this case you are accelerating with constant acceleration a for a time t so the initial velocity is zero and the final velocity is v. That means the average velocity is ½v.
Then distance travelled is the time multiplied by the average velocity so it's s = ½vt.
But this still has nothing to do with Einstein's equation.
If you start from rest and accelerate at constant acceleration a for a time t then s is the distance travelled. It isn't obvious what you mean by s_avg. The distance travelled is just the distance travelled. What would the "average distance travelled" be?
okay, but if I start driving my car and you have a stop watch, and you record my speed at the moment you turn off the stop watch, that is my final velocity, yes?
Assume I'm driving in a straight line. I've gone a certain distance in a certain amount of time
I'm sure you are very skilled at manipulating symbols, but you aren't so great at putting the meanings of those symbols into words. I don't understand how this can be, since the point of physics is to describe the real world—as opposed to pure mathematics
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Hi everyone. I have a question about the microcausality condition in QFT, i.e. the commutator of any two operators vanishes for space-like spacetime intervals. Is this a relation holding in any Lorentz invariant interacting QFT or there could be a priori a violation of it?
In other words, under what circumstances the microcausality condition holds for interacting fields? Weinberg states that is a sufficient condition to have a Lorentz invariant S-matrix and he comments explicitly that it is not necessary. What other kind of Lorentz invariant theories he is talking about?
I have mixed feelings about this answer. On the one hand, it correctly says that all electrons are the same. OTOH, it tells the OP to "Imagine [electrons] as small rotating balls". I don't think that's a good idea, but is it bad enough to warrant a downvote?
@ACuriousMind thank you. Let's put aside axiomatic QFT. What if microcausality is not satisfied in a local relativistic QFT but still the S-matrix is Lorentz invariant? Do we have counterexamples?
This paper arxiv.org/abs/0709.1483 is claiming that "For a Lorentz-invariant theory microcausality can be proven in a variety of ways"
I am not aware of any of this variety of ways they are talking about, since they refer to the vev of the commutator.
Could it be possible, in principle, to have a relativistic QFT, compute the spectral density of the two-point function and find that the field commutator doesn't vanish for space-like intervals? Or the computation would be automatically consistent with the microcausality requirement?
@ACuriousMind you don't need to know anything about the paper. It's just a statement about the fact that microcausality can be proven non-perturbatevely (and they cite the textbook of Weinberg)
No sorry, I think the spectral density has nothing to do with it. Still, I am wondering whether an explicit computation at one-loop of the two-point function could reveal a violation of microcausality.
As far as I understand it locality is the rejection of action-at-a-distance. By this I mean that in a given frame of reference at a given instant of time (in that reference frame), two physical objects can only interact if they are in physical contact. Lorentz invariance requires that this is the...
@vzn thanks for the link. @ACuriousMind you wrote "Only for very few and low-dimensional theories, e.g. scalar fields in 2D, it is proven that a theory with arbitrary polynomial interactions obeys the Wightman axioms". Do you have a reference about this fact of scalar theories in 2d?
@apt45 The classic is Glimm and Jaffe's work, e.g. in their book Quantum Physics. They construct the 2d theory as a Euclidean theory obeying the OS axioms, which via OS reconstruction means there is a corresponding Wightman theory. Note That I was talking there about the full list of Wightman axioms - it can well be that microcausality alone without the rest is much easier to establish
honestly am having trouble parsing the defn of "microcausality". this pg en.wiktionary.org/wiki/microcausality defines it as "The spacelike local commutativity or anticommutativity of fields." in a sense, A or Not A. but everything satisfies A or Not A...
Whether commutativity or anti-commutativity is the "correct" way to express causality depends on whether or not you have a fermionic or a bosonic field. See physics.stackexchange.com/q/134577/50583 for a formal derivation of why fermions must anticommute
@ACuriousMind therefore when we talk about Local field theories this is equivalent of talking about commuting fields at space-like intervals? So when the commutator is not zero we really talk about a non-local theory?
Or local QFT is more referred to local Lagrangians?
Yeah sure, this is the root of confusion about this topic. So, if I deal with a Lagrangian where the interactions are polynomials in fields and their derivatives, I might have in principle a violation of microcausality of the underlying quantum-theory?
Perhaps? I haven't really thought all that much about that condition - as I said, I only think that we can't prove it in full generality, I don't know any counterexamples
@expikx You have to be more precise in what you mean by that, and the answer is likely "we don't really know" in any case. In general, we do not understand interacting QFTs or their bound states very well and have to use some QM approximation (physics.stackexchange.com/q/217575/50583). Additionally, much of what you think of as a bound state in ordinary QM becomes a resonance in QFT (physics.stackexchange.com/a/12571/50583).
I have been deterred to ask for a brief translation of an old physics Russian paper in the stack. Is it valid to ask such a question according to the policies of the site? If not, could it be worth to include such questions?
I'm thinking only in certain paragraphs in the paper that could be of i...
In the past week, I've had two different questions closed as homework questions. In both questions, I included textbook problems that motivated my conceptual question, but in neither case was solving the textbook problem the essence of my question. I am concerned that the moderators, seeing that ...
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