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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Thu Jun 23, 2011 2:00 pm UTC

Yakk wrote:Don't be so hyperbolic.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Mr Scrotier » Thu Jun 23, 2011 2:11 pm UTC

Very interesting. So the universe can expand faster than the speed of light, but nothing can travel within it that fast. So... there must be a ring of nothing around the inside boundary of the universe?

Im picturing a reverse doughnut, where (travelling from the inside out) all the matter and particles and stuff are the "hole". Then you come to the doughnut itself, which is empty universe that represents the area where the universe has expanded before anything has had time to travel into it. If so, can there be any difference between the outside boundaries of the universe and the 'nothing' that is outside it?

Im predicting confusing answers about spacetime and how it is kind of something but not really.


On another note, massless particles always travel at the speed of light. Does this mean they will all travel the exact same speed through every medium? Gravity travels at the speed of light, is this the reasoning behind the supposed existence of the gravitron?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Thu Jun 23, 2011 2:38 pm UTC

Mr Scrotier wrote:Very interesting. So the universe can expand faster than the speed of light, but nothing can travel within it that fast. So... there must be a ring of nothing around the inside boundary of the universe?
No. First, there is no (known) boundary of the universe. When we say "the universe was the size of a teacup", what we mean is that everything in the currently observable universe took up that much space.

Second, no, because the expanding space carries all the matter along with it. This is why galaxies far away from us are getting farther away from us.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby firechicago » Thu Jun 23, 2011 2:46 pm UTC

gmalivuk wrote:1) Information would travel at the speed of sound through whatever material you made your tube with. Positing an indestructible material (by which I assume for this question you actually mean perfectly rigid) breaks relativity precisely because it would allow instantaneous information transfer. So positing such a material is equivalent to just going all the way and saying "What if we *could* send information instantaneously?"


To clarify further, any real or theoretically possible material is held together by one or more of the fundamental forces. (Generally electromagnetism, but some exotic theoretical materials like Neutronium are held together by other forces.) All of these forces operate at with the speed of light as a hard limit. In fact, light is a form of electromagnetic radiation. So for your hypothetical perfectly rigid material to exist and to carry information faster than the speed of light, it must be held together by a force which is itself faster than the speed of light.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Mon Jul 18, 2011 3:41 pm UTC

This thought has just occurred to me.

Obviously, once you cross the event horizon, there's no coming back. This, combined with colour charge confinement got me thinking.

If we have a meson with its centre of mass sitting on the event horizon with (lets say) the antiquark inside the event horizon and the quark outside with the meson having the escape velocity of the quark (so a velocity stupidly close to the speed of light because it's very close). In this case, the antiquark surely has to fall into the black hole, but the quark equally has to escape to infinity.

In this case, in order to keep colour charge confined, it's obvious that a new quark and antiquark are produced from the energy put into the field, the new quark forms a new meson with the antiquark and continues to fall into the black hole and the new antiquark forms a new meson with the quark and continues to fly away from the black hole.

But hang on. As the initial meson was being torn apart by the quark & antiquark's inertia and weight, it was losing kinetic energy to put into that field which eventually produced the new quark/antiquark pair. This loss in kinetic energy means that the new meson outside the black hole no longer has sufficient kinetic energy to escape and will (eventually) fall back into the black hole.

That seems a little odd since we initially supposed that the quark outside the black hole had sufficient energy to escape yet it still ends up inside the black hole. Is this right?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 4:15 pm UTC

Yeah, looks weird. This is a sign that you have to actually do the QCD in Curved Space calculation. I'm not volunteering, as I know very little about the actual mechanical implementation of quark confinement, much less how to put it in curved space.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Mon Jul 18, 2011 4:52 pm UTC

That's what I was afraid of. I guess I'll have to wait a few years then. *Adds to list of interesting problems*
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Mon Jul 18, 2011 7:00 pm UTC

Tricky! I'm no expert in black hole thermodynamics and I don't have the answer to this puzzle, but I'd like to make a few comments anyway. :)

You really need GR to determine the trajectory of objects near event horizons, and QM and GR do not play well together.

If the BH is small, the motion of the meson will be perturbed by Hawking radiation, and also the tidal force acting to split the meson will be greater than it would be for a large BH.

The Heisenberg Uncertainty Principle enters into this puzzle in a few different ways. Firstly, there's uncertainty relating to the exact location of the event horizon (EH). An EH is not a nice mathematically crisp spherical surface. The "radius" of the EH is a function of the mass of the BH. So to determine the radius of the EH precisely we need to know the mass precisely. But the more certain we are of the mass of the BH, the more certain we are of its momentum, and the HUP puts a limitation on how precisely we can know both the momentum and the position simultaneously. So we have a problem in trying to locate our meson precisely at the EH.

And then there's the problem of uncertainty in the positions and momenta of the meson's component quark and anti-quark. If they have well-determined positions above & below the EH, then their momenta will be fuzzy, so their trajectories will not be well-determined. Conversely, if we put the meson into a state where the momenta are what we need them to be in order that one of them gets swallowed by the BH and the other can escape, then their positions will be smeared, and we won't be able to say that one is above the EH and one is below.

And I guess we need to consider that the meson doesn't just contain the two quarks, it also contains the gluons binding them together. Gluons also have a color charge, and hence are also constrained by color confinement. As the meson is ripped apart the amount of energy in the gluons increases, but since this is all happening at the EH of a BH, some of those gluons will get stuck below the EH.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Mon Jul 18, 2011 7:27 pm UTC

So, besides the fact that I need both GR and QM, I might be asking the universe to be more certain than it can be. That's reassuring. I hadn't considered the gluons holding them together either, interesting.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 7:37 pm UTC

Oh, it can be sufficiently certain. Something does happen. A Meson either reaches the asymptotic future, or it doesn't.
The hard part is setting up your initial state.
What you probably want to do is set it up where a meson is sent from the asymptotic past on a trajectory that should "just skim" by the EH.
You can use a very high mass BH, so that where the EH is, the local gravity is actually weak. This keeps you from having to worry about quantum gravity at all, and just the interaction between classical gravity and a quantum object.
You do very much want to be doing a field theory calculation, rather than using any pointlike approximation for the meson components. Confinement is implemented at the fully sloshy fieldy level.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Mon Jul 18, 2011 7:45 pm UTC

So the ridiculous speed at which you have to be moving doesn't mean you'll have to factor relativity in?

I suppose the energy depth of "just skimming then escaping" the black hole doesn't change between a large and a small black hole much. The "steepness" of the change in gradient will be larger with a small hole, even. (I'm just wondering how much you'd have to care about the ridiculous speeds required)
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 7:58 pm UTC

Yakk wrote:So the ridiculous speed at which you have to be moving doesn't mean you'll have to factor relativity in?

Oh, you certainly have to care about special relativity and the effects of doing quantum field theory in curved space. But you can ignore back reaction.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Mon Jul 18, 2011 8:05 pm UTC

Yakk wrote:So the ridiculous speed at which you have to be moving doesn't mean you'll have to factor relativity in?

I suppose the energy depth of "just skimming then escaping" the black hole doesn't change between a large and a small black hole much. The "steepness" of the change in gradient will be larger with a small hole, even. (I'm just wondering how much you'd have to care about the ridiculous speeds required)

Sure, you need relativity, since escape velocity approaches c as you approach the EH, but by using a nice big BH you can keep things simpler, and mostly in the realm of SR rather than requiring the full machinery of GR. Combining QM with SR is do-able, combining QM with GR in highly curved spacetimes is where things get horrible, partly because we don't know how to quantize the gravitational energy properly. Fortunately, it's not too bad in this problem, since our meson has almost no gravity of its own.

The "steepness" is much worse with a small BH than a big one, and that steepness makes it tricky to calculate, but OTOH, the steeper the gradient, the more effective the EH is at separating the meson into its quarks.


A question I didn't make explicit in my first post: how do we get the meson to the location we want with the momentum required? The radius that photons orbit a BH is 1.5 times the Schwarzchild radius, IIRC. So the initial trajectory of our meson is a little tricky.

* checks wiki *
http://en.wikipedia.org/wiki/Photon_sphere

Oh, good I did remember correctly. :)

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 8:51 pm UTC

Right, you don't want an initial state as an orbit, you want to do a scattering problem.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Mon Jul 18, 2011 8:55 pm UTC

Hmm. So the "distance" that you have to get to the BH goes up as the BH mass/radius goes up. In effect, isn't it something analogous to "tidal" forces (ie, the steepness of the local gravity gradient) that tears your subatomic particle apart?

... but ya, a large enough black hole should make the attraction of the BH to the meson trivial. I hope.

...

Couldn't you "drop" the meson in on the relativistic equivalent of a hyperbolic trajectory?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 8:58 pm UTC

Yakk wrote:Couldn't you "drop" the meson in on the relativistic equivalent of a hyperbolic trajectory?

Yeah, that's the scattering I meant.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby collegestudent22 » Mon Jul 18, 2011 9:20 pm UTC

PM 2Ring wrote: But the more certain we are of the mass of the BH, the more certain we are of its momentum, and the HUP puts a limitation on how precisely we can know both the momentum and the position simultaneously. So we have a problem in trying to locate our meson precisely at the EH.


See, now this I have always thought is in direct contradiction to relativity. Relativity, as far as I understand it, states that I can arbitrarily define the reference frame of the BH as having zero momentum. Does this then mean that it could be anywhere, including in my living room, instead of this hypothetical point in space somewhere? Clearly not, as I can easily observe that it is most definitely NOT in my living room. So what gives?

Or do I have to define my individual reference frame as inertial with regard to everything else for my observations to make sense? In which case there is a preferred frame of reference, in a sense - the one in which the individual is making observations is preferred by evidence of their observations. Note this is still relative, but not in a completely arbitrary way, though.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Jul 18, 2011 9:22 pm UTC

If you want to apply quantum mechanical uncertainty to the curvature of space, that is when you definitely need quantum gravity (and not to just have some quantum field, like the meson, fly around near a classical black hole).
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Mon Jul 18, 2011 9:52 pm UTC

So it should be a bit easier with a large black hole?

I'll have to note that down. As I say, such a calculation is beyond me at the moment (I haven't even started my degree yet) so I'll have to put it to one side until I can.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Jul 19, 2011 12:16 am UTC

This is not only a PhD project, it is a difficult one at that. I do scalar fields in curved space. Quantum chromodynamics in curved space... I will buy you a beer.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby scratch123 » Fri Jul 22, 2011 2:53 pm UTC

I hope its ok to post a QM question here. I don't think it is important enough for its own thread.

I am having trouble understanding the idea of negative amplitude for a wave. Amplitude has to do with height right so I am having trouble understanding how that can be negative. When you square the amplitudes you get probability so why even bother with waves in the first place?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Fri Jul 22, 2011 4:26 pm UTC

Heights can be negative if you define the equilibrium height as zero (a common convention!) Then negative amplitude just means you dipped down.
In quantum mechanics is where you get the probability interpretation for the square amplitude. We don't square directly, because the probabilities don't add right: it's the psis that add. Heuristically:
P(A) = psi(A)^2
P(B) = psi(B)^2
P(A+B) = [psi(A)+psi(B)]^2
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Sir_Elderberry » Sun Jul 24, 2011 3:42 pm UTC

scratch123 wrote:I hope its ok to post a QM question here. I don't think it is important enough for its own thread.

I am having trouble understanding the idea of negative amplitude for a wave. Amplitude has to do with height right so I am having trouble understanding how that can be negative. When you square the amplitudes you get probability so why even bother with waves in the first place?

Remember that amplitude can be more than height. It's just a value that gets defined in space as a function of (usually) space and time. For example, think of an electromagnetic wave. It has an amplitude, which can be negative, but it's important to remember that even though we draw little vectors pointing different directions, there isn't really any space filled by those vectors. Wavefunctions take negative values, but it doesn't mean they literally "dip down". Waves of water or string have height-amplitudes, but there are lots of kinds of waves and therefore lots of things that can be assigned amplitudes.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby tommyboy611 » Tue Aug 02, 2011 1:28 pm UTC

I just recently (within the last year or so) really got the hang of relativity and it implications, so I'm a bit new to this. My question is that if, say, you had two objects that travel past each other with 1/2c, won't one object, from the other object's inertial frame, be travelling at the speed of light? I've been thinking about this and it probably has a simple answer, but it illudes me.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Aug 02, 2011 1:34 pm UTC

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby tommyboy611 » Tue Aug 02, 2011 2:01 pm UTC

Right? So the equation to find the velocity of the object would s= (velocity of object 1) + (velocity of object 2)/1+(v1v2/c); which I guess would reduce to s=c/~74948115. I don't know if the math is spot on, but thanks for showing me that.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Aug 02, 2011 4:20 pm UTC

Ah, remember, you are dividing by c^2.

So if v_1 = c/2, and v_2 is c/2, you are getting that each sees the other moving with
(c/2 + c/2) / (1+1/4) = 4 c / 5 .
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Tue Aug 02, 2011 4:49 pm UTC

[ This is a C&P from a post I made on another forum.]


Velocity is the gradient of a particle's worldline in Minkowski spacetime.

Just as in normal Euclidean space, if you simply add the gradients together of two slopes you won't get the correct value for their combined gradient.
For example, if we have a wedge with a slope of 2/10 (2 units vertical per 10 units horizontal) and sit it on top of a wedge with a slope of 1/10, the combined effect will not be 3/10. You have to convert the slopes to angles, add the angles together, and convert back to slopes.

With a bit of trigonometry, we get this handy formula for the combined slope:

w = (u + v) / (1 - uv)

So for my previous example
w = (0.2 + 0.1) / (1 - 0.1 * 0.2)
= 0.3 / 0.98 ~= 0.30612245

As you can see, the combined slope is only a tiny bit greater than the simple sum, but if we used steeper wedges the discrepancy would be greater.

In Minkowski space, the formula is slightly different, because the time dimension is different to the space dimensions:

w = (u + v) / (1 + uv)

where u & v are the velocities we are combining, and w is the resulting velocity. All of these velocities are measured relative to c, in other words, they are in units such that c is equal to one.

Plugging in the values from the previous example, if we have a spacecraft traveling at 0.2c, relative to some observer, and it launches a probe in the same direction that it's traveling with a speed of 0.1c, the observer will measure the probe as having a speed of

(0.2 + 0.1) / (1 + 0.1 * 0.2)
= 0.3 / 1.02 = 0.29411765

Here, the combined speed is only a tiny bit smaller than the simple sum, but if we used higher speeds the discrepancy would be greater.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Robert'); DROP TABLE *; » Wed Aug 03, 2011 5:36 pm UTC

This sounds like a really basic question, but when I tried to work it through myself I got lost. Simply: What's the mass/energy of a given rest mass's gravitational field? I got confused, because although I know that two masses posses gravitational potential energy, but surely that energy in turn has G.P.E.? ...Actually, now I'm even more confused, because originally I forgot that GPE is negative, and so the GPE of two masses' GPE would be positive.

Am I up the wrong tree here, or what?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Thu Aug 04, 2011 7:54 pm UTC

Robert'); DROP TABLE *; wrote:What's the mass/energy of a given rest mass's gravitational field?

Relative to what?

http://math.ucr.edu/home/baez/torsors.html

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Robert'); DROP TABLE *; » Fri Aug 05, 2011 6:03 pm UTC

PM 2Ring wrote:Relative to what?

http://math.ucr.edu/home/baez/torsors.html

Empty space? I think that's well-defined.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby WarDaft » Sun Aug 07, 2011 10:10 pm UTC

Well, one way to make delta-E on the big bang zero, is to have the total gravitational energy of a particle be equal to the negative of the particle's energy. I think that's sort-of what they're talking about here by vanishing 4-divergence, but IANAP.



I personally have always wondered why uncertaintly isn't in some way proportional to relative mass. Suppose you were trying to measure the position of a green bowling ball in the middle of a large room, by bowling otherwise identical red bowling balls at it hoping to hit it... while blindfolded... and attempting to derive the position of the green bowling ball from the sound it made from hitting one of ten large gongs around the border of the room. If this was the only way physically possible to detect a green bowling ball (however silly a concept that is) would green bowling balls then start to exhibit properties of uncertainty just as fundamental particles do?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Mon Aug 08, 2011 2:20 am UTC

Robert'); DROP TABLE *; wrote:
PM 2Ring wrote:Relative to what?

http://math.ucr.edu/home/baez/torsors.html

Empty space? I think that's well-defined.

Maybe not as well-defined as we need for this problem: it's a bit difficult to pin down locations in empty space in a way that all observers will agree on. So even if you say that the test mass is at rest relative to some region of space that you identify as surrounding it at time t=0, another observer can validly claim that the test mass has a non-zero velocity & hence non-zero kinetic energy and momentum relative to that same region.


I hope you didn't get the impression that I was disagreeing with your statement that gravitational energy has gravitational energy. Fortunately, gravity is quite a weak force, so the amount of energy "stored" in the warping of spacetime is fairly small in relation to the rest energy of the body doing the warping, at least until you get up to the neutron star / black hole level.

I was hoping that Doogly would make a comment about the recursive nature of gravitational energy calculations, since he's our local expert on curved space.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Aug 08, 2011 4:47 am UTC

So, gravity can interact with gravity. But only in a very special way.

You absolutely do not take some spacetime, figure out the gravity there, define some stress tensor for it, and use that as a source for more gravity. In fact you can't define a stress tensor for it, and this is something that might bother people. (The fact that we can't define entropy of a gravitational system bothers some more people.)

Instead, all of the gravitational self interaction has in a sense already been summed up to give us the Einstein field equations, which are nonlinear. Nonlinearity is what makes GR difficult, and it captures the interaction of gravity with gravity. For example, in Newtonian gravity, you can get the gravitational field of a configuration of multiple particles by adding up the Gm_i/r_i^2 for each particle i. In GR, not so. You have a nonlinear thing to solve.

But that's where all the work is. You don't have to do an extra bit of work after this (thank heaven)
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Tue Aug 09, 2011 8:29 pm UTC

To be clear, and I ask this because I think I have seen it used both ways, does "classical physics" refer to physics before Newton, as opposed to relativity and quantum mechanics; or does it refer to physics except for quantum mechanics, including both special and general relativity?

Or can it be used either way, and this question was therefore pointless?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Aug 09, 2011 9:01 pm UTC

Generally classical = not quantum, so GR is classical.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Sir_Elderberry » Tue Aug 09, 2011 9:22 pm UTC

I've always thought of it as "physics, pre-1905" but Wikipedia says you can use it either way.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby phlip » Wed Aug 10, 2011 7:57 am UTC

It depends on the context... in a discussion of Complicated Theory X, "classical physics" refers to the simpler models we used before Theory X was developed. So in a conversation about SR it means Newton, in a conversation about GR it means SR (or Newton). In a discussion of QM it means anything non-quantum. If string theory ever gets going, then standard-model QM could become "classical" (assuming it's simpler than ST turns out to be).

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby collegestudent22 » Sat Aug 13, 2011 1:13 am UTC

My experience in college physics courses have shown me that "classical physics" actually means, "all the stuff you should already know from previous classes that we are now throwing out for more complicated stuff".

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Dopefish » Sat Aug 13, 2011 1:37 am UTC

In most of my experiances classical=not quantum, and relativity is thus classical. For things not including relativity, it's usually mentioned explicitly as 'non-relativistic', so you get things like non-relativistic quantum theory and lots of classical books saying things like 'treating the particle non-relativisticly...'.

Of course, it's often clear from context, as anything dealing with relativity seems to quickly spawn v/c's all over the place. (To be fair I don't know GR or QFT so I don't know if the relativistic aspects manefest themselves in a different way there. If it doesn't show up as v/c's though, it's probably something worse and even more distinctive from non-relativistic stuff.)


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