elfmotat

Is this forum here to ignore my questions,

although I answer yours?

If you keep making claims without evidence, yes.

Please give me the math example I requested.

I will take it from there if worthy.

I don't really understand what you're asking for. The nearest thought to my mind would be the following example:

[math]y = x^2[/math]

If we introduce a displacement [math]\Delta x[/math], then we have:

[math]\Delta y = (x+\Delta x)^2 - x^2 = 2x \Delta x + (\Delta x)^2[/math]

or:

[math]\frac{\Delta y}{\Delta x} = 2x + \Delta x[/math]

This is well-defined for all [math]\Delta x \neq 0[/math]. But, the whole point of calculus is the concept of the limit. If we take the limit as [math]\Delta x \to 0[/math], then:

[math]\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x} = \lim_{\Delta x \to 0} 2x + \Delta x = 2x[/math]

We simply define:

[math]\frac{dy}{dy} := \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x} = 2x[/math].

Is there something wrong with what I just did? If so, why/how? That's calculus, at its most basic. Alternatively (and more hand-wavy), we can introduce an infinitesimal displacement [math]\Delta x = \epsilon[/math] such that [math]\epsilon^2 = 0[/math]:

[math]\Delta y = (x+\epsilon)^2 - x^2 = 2x \epsilon + \epsilon^2 = 2x \epsilon[/math]

or:

[math]\frac{\Delta y}{\Delta x} = 2x[/math].

Is this what you're taking issue with? The introduction of a number such that its square is zero? Both of these methods can be made much more rigorous and well-defined. There is nothing logically inconsistent here, unless you'd care to point out the flaw?

The force of gravity does not become infinite at the event horizon. (It is not clear what it is - or if "force of gravity" has any meaning in this context.)

I agree that "force of gravity" is poorly defined in GR, but there are a few meaningful ways to interpret what it means for a Schwarzschild BH. For example, the "force required to hold a particle stationary at a particular r-value." This force does indeed go to infinity as r->2M.

 

Could I put it another way, if it were possible for an observer to position himself in the gap, from his perspective would the combined speed of the objects close to c close the gap at excess of c+?

 

Thank you!

The observer could measure the distance between the objects shrinking at >c. Note, however, that the rate of distance shrinkage isn't actually the velocity of anything. It's not even a velocity, though it does have the units of velocity. The objects themselves would measure each other to be moving at <c.

So if they both know that they will measure opposite spins, then when Bob makes the final measurement to be say (spin up) then they would know that Alice must have gotten say (spin down) ?

 

Also thank you for the response Strange

Yes!

1) By looking at 2 locations and pre-informing both Alice and Bob while by removing relativistic properties it becomes easier to go into moving along with the design stages of the idea. Taking a bottom up approach if you will. I am not dis-counting there importance, the opposite in fact. I am maintaining relativistic properties in there extremes and uses them as a comparison check, however again I am currently designing upward so I need to consider the most perfect conditions.

I'm still not sure why it matters if they make their measurements simultaneously or not. Could you explain why this would impact the experiment?

2) I am assuming that both inertial frames S' are moving at the same velocity in respect to an observer S( Please correct me if I am incorrect ).

You can assume whatever you'd like. Relativity tells us that if two events happen simultaneously in one frame, they do not and cannot happen simultaneously in any other frames. So you can set up the experiment so that Bob and Alice are at rest w.r.t. each other, and so that they make their measurements simultaneously in their rest frame. The fact that they made their measurements simultaneously in this frame is physically irrelevant, because there are an infinite number of equally valid frames in which they don't make their measurements simultaneously.

I am assuming that both Alice and Bob are pre-informed that a measurement is going to occur at a certain period of time.

When this time is reached first Alice will measure there entangled particle,and Bob will measure there's.

 

Under these circumstances I believe that once Alice measures the entangled particle, the wave function will collapse for each pair, therefore causing Bob's particles wave function to already be collapsed before even being measured. ( Please Correct if Wrong )

 

That way they would not need to compare with one another because they know when they are measuring and what they are looking for. So if Alice measures the first entangled particle to be say (spin up) then the particle will have collapsed and the entangled particle with Bob will be (spin down) even before Bob measures it.

 

So there is no need to check for a comparison because they both know that Alice will measure first causing the entangled pair to decay and that Bob will measure second. So whatever Bob measures they will know that it is the opposite spin value as the Alice's.

The point is that there's no way for Bob to tell if the wave-function has collapsed until he makes his measurement. And once Bob makes his measurement, he is also causing wave-function collapse.

Yes, however what if both Alice and Bob have previously confirmed with one another that they would measure there own particle respectively ( Alice has particle A Bob has particle anti-A, anti just meaning the entangled particle and not meaning the actual anti-particle ) at the "same time." Meaning that at any distance, whether it be defined or undefined, both Alice and Bob would have measured these two entangled particles at the same instance in time regardless of relativistic properties.

 

1) Why do you think this would make a difference?

2) If they measure at "the same time" in their rest frame, they won't measure at the same time in a frame moving w.r.t. them.

If he observes/measures it then he is also causing wave-function collapse!

Obesity is strongly linked to low T. Society has gotten much fatter, so I'm not surprised that T-levels have also dropped. It would be interesting to see a study on how much of the T-level drop can be explained by increased obesity rates.

Well, r^2 can really reduce the force acting by m1 and m2 according to the Newtonian description.

What do you mean? Are you under the impression that spacetime curvature is not dependent on your distance from a gravitational source? Because it is.

I agree that you cannot plug in an infinite value for either of the masses.

While this is true, I'm not sure how it's relevant. I never said anything of the sort.

Right well the mass creates a field which produce gravity acting on the other masses, speculation

No, not speculation, fact. This is what we observe.

 

Yes the influence of the gravity from the sun goes a long way on object of different mass. If you do the Newton's gravitation's calculation it should work out here. My focus is that I don't think the spacetime in Neptune is bent by the sun.

Newtonian gravity is an approximation of General Relativity when gravity is weak and objects are moving slowly compared to light. So, obviously, they need to agree on the range of gravity. If Newtonian gravity's range is infinite, GR's range must also be infinite. Whether or not you think it's true is irrelevant to whether or not it's actually true.

Like a magnetic field exerting current on a wire, speculation

What speculation? Electromagnetism is described by 1) field equations which describe how the EM-field behaves, and 2) an equation of motion which describes how objects behave when they interact with the field. Similarly, GR is described by field equations and an equation of motion. There is no speculation -- observation fits these models.

An increasing function is a function where [math]f'(x)>0[/math] for all [math]x[/math]. So you need to find a way to prove that the derivative of the function is always greater than zero.

(Hint: this will be easier to see if you combine those fraction terms into a single fraction.)

I'm allowed to oversimplify physics- I'm a chemist.

However, as you have pointed out, the "particles" are only a handy way to visualise what's happening without doing "jolly hard maths" (JHM).

I can't imagine Eldad doing the JHM so he's stuck with an imperfect model .

(Nothing to be ashamed of- the JHM is over my head too; I used to be able to do time dependent perturbation theory, but that was many years ago, and I wasn't good at it then).

Sometimes there just isn't an easy answer.

True. I think the key (for Eldad and others) is to recognize when things are being simplified to make them easier to explain and visualize without the JHM, but that at the end of the day the JHM is what defines the theory. Many tend to take analogies, mathematical objects with physical-sounding names, etc., too seriously and derive meaningless predictions by extrapolation.

 

It's not the first time I've encountered this "I don't get it, so it should be changed" argument from Eldad. I've tried reason and I've tried encouragement. This time I tried to show the absurdity, but I guess I failed.

Fair enough. I haven't been around for a while, so I'm unfortunately no longer "in the loop" in regard to many users' habits.

What happens when one of a pair of virtual particles falls into a black hole?

I understand the point you're making (that this results in Hawking radiation), but really you're oversimplifying things a lot. It's not nearly so simple as "virtual particles are created, one falls in and the other is ejected." That's a nice picture that humans have an easy time visualizing, but again, speaking in terms of virtual particles only makes sense in perturbation theory. The full, non-perturbative model of interacting quantum fields on a Schwarzschild background would describe what's going on better, and with no such reference to internal lines on Feynman graphs.

OK, you don't understand it so we should rewrite all the text books.

well, it's a point of view...

 

Incidentally re "Even the photon isn't a particle"; well it sure acts like one.

In much the same way, the term "nose" is very confusing, since it sounds like it's a plural word, like "eyes", but you only have one of them. And "nose" sounds like it's intelligent, but it's not. It runs but has no legs, and it constantly smells.

 

Therefore, we need to start using the term "Donald" instead of "nose", because I said so.

I don't think you guys are being very fair. While I agree 'virtual particles' are well-defined (namely, internal lines in Feynman diagrams), and that it would be hard/impossible to change the term, I also think the term is confusing. See e.g. the link Strange provided.

Perhaps the biggest thing to note about virtual particles is that they only make sense in perturbative QFT. They are mathematical objects (propagators) that arise from a Taylor series approximation of the full theory. People (i.e. popsci documentaries) attribute much more meaning to them than they should really have.

What steps have you made to solve it? Are you given the equation for a catenary (/are you allowed to look it up), or are you supposed to derive it via calculus of variations? I remember the latter being pretty tedious.

I saw this recently:

Really it depends on what you mean by "destroy the moon." If you make your question more specific then you'll recieve more specific answers.

And it is completely beyond my ken to test it which is why I have come here to discuss it.

The issue is that there isn't a way to test it, even in principle. De Broglie-Bohm's predictions are completely equivalent to those of any other interpretation of QM.

A hunter sets off from his camp due South.

After travelling 50 mi he turns due West.

After travelling 50 mi he shoots a bear.

Then he turns North and, after travelling 50 mi is back at his camp.

What color is the bear ?

White.

If the new frame with its origin at the event [math](t,x)=(T,X)[/math] in the first frame is moving with velocity [math]v[/math] w.r.t. the first frame, then the new coordinates are given by:

[math]t' = \frac{t-T-v(x-X)/c^2}{\sqrt{1-v^2/c^2}}[/math]

[math]x' = \frac{x-X-v(t-T)}{\sqrt{1-v^2/c^2}}[/math]

If they are stationary w.r.t. each other then [math]v=0[/math] and this reduces to:

[math]t' = t-T[/math]

[math]x' = x-X[/math]

Hold up, why not just say dark matter itself causes variations in the gravitational constant instead of having two different theories try to predict the same kind of thing about gravity? It would give dark matter its accuracy and give MOND the mechanism.

When the gravitational constant is promoted to a field, the result is Brans-Dicke Theory. The new field must obey a field equation that constrains it to behave according to basic physical principles like Lorentz symmetry, locality, etc.

Modified gravity theories that attempt to reproduce observed galaxy behavior without dark matter like TeVeS are even more complicated, introducing a new type of vector field, a non-dynamical scalar field, and a dynamical scalar field like the one in Brans-Dicke Theory. Gravity theories of this sort have largely been ruled out as they fail to explain behavior like the gravitational lensing in the Bullet Cluster.

True but what about other theories of physics like statistical mechanics (both classical and quantum), thermodynamics, chaos theory, dynamical systems etc?

 

Do all these theories have a an equal amount of experimental evidence supporting them like general relativity and quantum mechanics for example?

They are all well-tested fields of physics. Keep in mind that different regimes require different physics. For example, you'd never use Newtonian mechanics to describe how electron orbitals behave - you need quantum mechanics for that, because Newtonian mechanics doesn't apply to systems that small. That doesn't mean NM is 'wrong' or 'less tested.'