A miscellany of physics

[Creation]

Apech kindly invited me to start a new thread in which I address some questions of Owledge on physics.

 

How does that Einstein equation demonstrate that mass of a particle is just a form of energy? To me it shows the opposite: that energy is nothing but the observed effect of mass in motion.

 

Can someone explain to me how particle accelerator experiments where electromagnetic fields accelerate a particle to near light speed and need more and more energy for every little bit are showing that the 'mass' (the other one) of the particle increases? Excuse me - how fucking crazy is it to try and accelerate something to or above light speed using a force that is fueled by a sub-light speed phenomenon (electricity)?

 

The point here is how to define mass. What is mass? We have our intuitive notions, but when claims are made about a particle's mass increasing as it's velocity increases, there must be a precise definition of mass, or more exactly an operational definition: what do you do to measure it?

 

It is experimentally observed that if you apply a force to an object, it accelerates in the direction the force is applied (Newton's second law). The acceleration induced by a force will be half as much for something twice as big. So let's define a quantity called mass that makes this precise. There is a standard of mass, say a kilogram, and if you push the kilogram standard and some other thing with the same amount of force, and the standard accelerates n times faster than the other object, say that object has a mass of n kilograms. There is a bonna fide operational definition. But of course, this requires an operational definition of force and acceleration along with the truth of Newton's second law to work.

 

What Einstein was especially good at was really thinking deeply about things just like this: what things like mass, velocity, etc. really mean, how we measure them, just what assumptions go into that measurement, and how valid are those assumptions. He was intensely studying Mach, Hume, and Kant with his non-physicist buddies at the time he developed special relativity, and those two activities were quite related.

 

So, as you may have heard, in special relativity it is said that a particle traveling at less than the speed of light cannot be accelerated to the speed of light or faster. According to Newton, if you keep pushing with a constant force it will accelerate at a constant rate and eventually exceed the speed of light. So does relativity contradict the second law of motion? Not if you are willing to challenge your assumptions about mass. What you see in a particle accelerator is that if you push an electron with a constant force, it does not accelerate at a constant rate, but the acceleration decreases as the electron goes faster. And as the electron gets closer and closer to the speed of light the acceleration gets smaller and smaller so that the electron never reaches the speed of light. Now by our operational definition of mass, this means that the electron's mass increases the faster it travels, becoming infinite at light speed, which is impossible.

 

Moving along, here is one of the big causes for misunderstanding of relativity. People hear about E=mc^2 and think that because mass is a form of energy, the aforementioned mass increase is due to the increase in kinetic energy of the electron. But in the reference frame of the electron, like a person sitting in a train not considering themself as moving, the electron is not moving and has the same mass it has always had. So this mass increase is not what E=mc^2 is talking about. That is something different. The confusion is that there are two inequivalent definitions of mass. The second is this: measure the mass in a reference frame where the particle is not moving. This will be the same no matter how fast the particle is going, because you first catch up to it before measuring. This is called rest mass.

 

What E=mc^2 is really saying is that rest mass can be converted to energy. So if a particle emits light in all directions equally so there is no recoil and therefore it stays at rest, it's mass nevertheless will change: it will lose mass to account for the emitted energy. But E=mc^2 is only valid if the particle is at rest. The general case is

 

 

where p is the momentum and m is the rest mass. If p is 0 it reduces to E=mc^2.

 

Notice that if m=0, then E=pc. This is the equation that holds for, say, a photon. Which is to say, all of light's energy comes from it's momentum, not from any mass content. I once talked to a guy who was absolutely convinced that light had to have mass because it had energy and E=mc^2. I tried to explain that E=mc^2 is only valid for particles in their rest frame (i.e. when you have caught up to them), and that particles traveling at the speed of light do not have a rest frame because you can't catch up to them, so E=mc^2 doesn't apply to light.

 

Owledge called the idea that light doesn't have mass "weird" but I'm nor sure why. You can't accelerate or decelerate light by pushing or pulling on it, so how could it be said to have mass? Mass is defined as the resistance to pushing or pulling.

 

Gravity is different than other forces because everything falls at the same rate in a gravitational field, no matter how heavy it is. Even things that other forces don't pull on at all, like light. This lead Einstein to the idea of gravity as the curvature of spacetime, and I might explain how that works some other time. I would also like to address the issue of the speed at which the electromagnetic force acts. That is a neat story too.

Edited April 1, 2012 by Creation

[Apech]

Bravo!

 

I think maybe some of the confusion for some people comes from the variety of types of particles that scientists talk about e.g. hadrons, leptons, baryons, bosons ... and so on. They are all ways of categorizing behavior and interaction. Using the word particle we still tend to have the image of a billiard ball ... i.e. something which in itself is hard and dense. But we also 'know' that this is not the case ... in fact hardness and density are characteristics of the macro world based on field energy interaction. There is no solid 'stuff' of which things are made. Atoms for instance are largely empty space.

 

We have a common sense view of the world which tells us that solid things are dependable and real ... and we have quantum mechanics (a kind of unfinished project) which tends to tell us the opposite. If it were not for the fact that so much of our modern technology (including our computers) relies on quantum mechanical effects in semi conductors for instance ... a lot of people would reject it completely out of hand as being absurd.

 

I can't remember which physicist it was who said 'forget the theory and do the numbers' (possibly Fred Hoyle) ... but that is what most scientists do. Those who do theorize start to produce interpretations which sounds like mysticism.

 

Just a couple of thoughts.

[doc benway]

Great job Creation.

Like they say, if you can't make something simple, you don't understand it.

That was a simple and elegant description - much appreciated.

I very much look forward to future contributions like that if you're willing.

I think it's helpful for us to understand the precise terminology and conventions as defined by physics because so many scientific terms are inaccurately used in the discussion of metaphysics and spiritual matters (particularly terms related to quantum mechanics).

[Birch]

Creation this is great!

I'm def up for readings about the other stuff!

 

Have you considered blogs/ebook/podcast...?

[Zhongyongdaoist]

I can't remember which physicist it was who said 'forget the theory and do the numbers' (possibly Fred Hoyle) ... but that is what most scientists do. Those who do theorize start to produce interpretations which sounds like mysticism.

 

Apech,

 

It was Richard Feynman and it was part of a longer quote expressing Feynman's warning about the deleterious effects of thinking about quantum mechanics, exactly that mystical sounding stuff that you note. Combining your paraphrase with one from http://www.physicsforums.com/showpost.php?p=2791842&postcount=41, we get something like the whole quote:

 

"forget the theory and do the numbers, If you try to understand it, it will drive you crazy."

 

I remember reading it twenty to thirty or so years ago as one of those quotes that often begin chapters in books. I have regretted for almost all of the intervening time that I wrote down neither the original quote's source or the book in which I read it. I found it a fascinating quote at the time because it reminded me of nothing so much as what a teacher of astronomy in the late 16^th or early 17^th centuries would have said about heliocentrism and the dangers of descending into heresy.

 

Unfortunately a web search does not pull up the original, perhaps because it shows how backward looking the 'great innovator' was. Feynman was never comfortable with the implications of quantum mechanics, or for that matter any interpretation of physics that undermined 'common sense' interpretations of the world.

 

I had gone back to review a great deal of this because of your own post (http://www.thetaobums.com/index.php?/topic/23026-anybody-care-to-comment-on-my-metaphysic/page__view__findpost__p__330124__hl__rutherford__fromsearch__1) which helped to create this thread:

 

Ernest Rutherford said: "All Science is either physics or stamp collecting"

 

...so make that monster post!!!!!!!!!!!!!!!! In fact start a new thread ... I promise to read.

 

Rutherford was looking backward to the reductionist determinism of Laplace. Feynman was still in thrall to Laplace's demon.

 

Regrettably, because I am too busy to take the time to pursue either of the posts In the detail I might wish, I must be satisfied with clarifying the source of the quote you mention. Anyone who can source the whole quote would be doing us all a great service and should they chose to post it, I thank them for it in advance.

 

Creation,

 

Thanks for an excellent post and for the willingness to create this thread. I look forward to reading more.

[Creation]

"forget the theory and do the numbers, If you try to understand it, it will drive you crazy."

In physics lingo, "theory" is the mathematical part, so it would be more like "forget the interpretation and do the calculation."

 

An actual quote that gets tossed around in physics circles is "Shut up and calculate". Usually attributed to Richard Feyman, but actually from David Mermin's "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be 'Shut up and calculate!'"

 

 

Great job Creation.

Like they say, if you can't make something simple, you don't understand it.

That was a simple and elegant description - much appreciated.

I very much look forward to future contributions like that if you're willing.

Thanks. Unfortunately, being able to make something simple doesn't mean you understand it. Every time I try to write explanations like this I am confronted by all the gaps in my knowledge. I just try to make sure that nothing I say is demonstrably wrong.

 

I think it's helpful for us to understand the precise terminology and conventions as defined by physics because so many scientific terms are inaccurately used in the discussion of metaphysics and spiritual matters (particularly terms related to quantum mechanics).

Yes! I completely agree.

 

Speaking of quantum mechanics, here is a relevant quote from Edwin Jaynes:

 

"Although Bohr's whole way of thinking was very different from Einstein's, it does not follow that either was wrong. In the writer's present view, all of Einstein's thinking - in particular the EPR argument - remains valid today, when we take into account its ontological purpose and character. But today, when we are beginning to consider the role of information for science in general, it may be useful to note that we are finally taking a step in the epistemological direction that Bohr was trying to point out sixty years ago.

 

But our present [Quantum Mechanical] formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature - all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple."

 

He specifically is talking about the meaning of the wavefunction. The two interpretations of Quantum Mechanics that I am most interested in take this in precisely opposite directions. The Causal or Ontological interpretation of David Bohm takes the ontological aspects of the wave function part as far as possible, and the Quantum Bayesian interpretation takes the epistemological aspects of the wave function as far as possible. I am watching research in both directions intently.

 

For some cutting edge research that indirectly gives insight into how the ontological interpretation works:

 

Yes indeed, a classical system that reproduces the effects of the double slit experiment and other phenomenon long thought to belong exclusively to the quantum domain. Mind blowing.

 

The idea that the both the particle and the wave are real and the wave guides the particle was exactly Louis de Broglie's idea about the meaning of quantum mechanics, and David Bohm independently came up with the same idea later. Now, Couder has shown that there is a macrosopic analogy of such a situation that does indeed reproduce many effect of quantum mechanics. So the question begs to be asked, "If quantum mechanics is closer to classical mechanics than we thought, then just what exactly is non-classical about it?" Bohm's later work was trying to understand exactly this. Some of his former collaborators have recently published on how his ideas about the meaning of quantum mechanics might explain the interface between mind an matter.

Edited April 1, 2012 by Creation

[Owledge]

@Creation

I was pointing at a level above the formula stuff, a meta-view so to speak, and discussing that would be too complicated and I am not versed in the complex physics formula jungle. I'm simply using my experience-tested intuition about when something smells fishy, so I remain doubtful and consider that there might be profoundly wrong assumptions involved. Usually when a complex of phenomena is explained with a formula, and then an exception is discovered and the same formula gets adapted to also include the new phenomenon, it looks like what some guy (forget who) cynically said about scientists trying to make reality obey their math.

 

I would also like to address the issue of the speed at which the electromagnetic force acts. That is a neat story too.

Even neater is talking about the speed of a permanent magnet field.

 

And can you explain why gravity acceletates things at a constant speed and why exactly it is the 9.81 m/s? From my experience, trying to figure out why nature works with a seemingly arbitrary number - understanding why it is not arbitrary, reveals profound secrets of the universe.

[Apech]

 

....

 

And can you explain why gravity acceletates things at a constant speed and why exactly it is the 9.81 m/s? From my experience, trying to figure out why nature works with a seemingly arbitrary number - understanding why it is not arbitrary, reveals profound secrets of the universe.

 

Because Galileo dropped them from the leaning tower of Pisa? ?

[zerostao]

http://books.google.com/books/about/Quantum_Geometry.html?id=T6fWst-KdoYC

 

ai yeah geometry still trumps physics/quntuam physics, however interesting the discussion of quantum physics is.

strange no one evr talks of quantum chemistry.

they all work together and all but

i say i say mathematics dont lie

[Owledge]

i say i say mathematics dont lie

It's a tool. Mathematics don't lie just as a gun doesn't shoot people. People shoot people and people lie.

[joeblast]

@Creation

I was pointing at a level above the formula stuff, a meta-view so to speak, and discussing that would be too complicated and I am not versed in the complex physics formula jungle. I'm simply using my experience-tested intuition about when something smells fishy, so I remain doubtful and consider that there might be profoundly wrong assumptions involved. Usually when a complex of phenomena is explained with a formula, and then an exception is discovered and the same formula gets adapted to also include the new phenomenon, it looks like what some guy (forget who) cynically said about scientists trying to make reality obey their math.

 

 

Even neater is talking about the speed of a permanent magnet field.

 

And can you explain why gravity acceletates things at a constant speed and why exactly it is the 9.81 m/s? From my experience, trying to figure out why nature works with a seemingly arbitrary number - understanding why it is not arbitrary, reveals profound secrets of the universe.

9.81 is just the slope of the earth's gravity well, change the massive body in question, change the slope.

[Owledge]

Thanks for reminding me.

Is there a gravitational acceleration constant in relation to mass?

Edited April 2, 2012 by Owledge

[joeblast]

Sure is

 

http://en.wikipedia.org/wiki/Gravitational_constant

 

[joeblast]

Even neater is talking about the speed of a permanent magnet field.

Maxwell already showed us why that is c

 

 

With regard to Einstien and Bohr, a good commentary from an astute physicist:

http://motls.blogspot.com/2012/03/einsteins-box-and-triumph-of-bohr.html

[Creation]

And can you explain why gravity acceletates things at a constant speed and why exactly it is the 9.81 m/s? From my experience, trying to figure out why nature works with a seemingly arbitrary number - understanding why it is not arbitrary, reveals profound secrets of the universe.

I think Newton would agree. He was the first to explain the 9.81 I think.

 

As it turns out, gravity does not accelerate things at a constant rate. The strength of the gravitational field generated by a spherical mass will vary by an inverse square law: if you double your distance from the center of the sphere, the field will be four times weaker. If you triple your distance, nine times weaker, etc.

 

As it happens, changing altitude by a few hundred or even a few thousand meters is actually a tiny change compared to the diameter of the Earth, so for all practical purposes, everywhere ordinary people find themselves the acceleration due to gravity will be 9.81 m/s^2. If you are on top of Mt. Everest or in a jet airliner, it will actually be slightly less (just looked it up: about 9.78 m/s^2 on Everest).

[Creation]

ai yeah geometry still trumps physics/quntuam physics, however interesting the discussion of quantum physics is.

I am not sure what you mean by this.

 

With regard to Einstien and Bohr, a good commentary from an astute physicist:

http://motls.blogspot.com/2012/03/einsteins-box-and-triumph-of-bohr.html

While that is a nice exposition, it has absolutely nothing to do with the quote about Bohr and Einstein I mentioned, which referred to understanding the relationship between the epistemological and ontological aspects of the quantum formalism (Bohr emphasizing epistemology and Einstein emphasizing ontology).

 

Maxwell already showed us why that is c

This thread was started for exposition, so feel free to explain how Maxwell showed us this. It is on my list, but I was going to talk about general relativity first, since zerostao likes geometry.

Edited April 2, 2012 by Creation

[joeblast]

I am not sure what you mean by this.

is he getting into string theory?

 

While that is a nice exposition, it has absolutely nothing to do with the quote about Bohr and Einstein I mentioned, which referred to understanding the relationship between the epistemological and ontological aspects of the quantum formalism (Bohr emphasizing epistemology and Einstein emphasizing ontology).

Sure you read the link?

 

This thread was started for exposition, so feel free to explain how Maxwell showed us this. It is on my list, but I was going to talk about general relativity first, since zerostao likes geometry.Naturally, by standing on the shoulder of giants (i.e. ampere) and grasping the pearl in the muddy water I dont have time to play lectures on physics right now though!

[Creation]

Sure you read the link?

Yes I'm sure.

 

If you would like to elaborate on how it is relevant to the relationship between epistemology and ontology in the quantum formalism be my guest.

 

Lubos himself says

"From that moment on, Einstein avoided attempts to prove that quantum mechanics was wrong; instead, he only tried to argue that quantum mechanics was an incomplete description."

 

The issue of completeness is a major part what I am calling the relationship between epistemology and ontology, and it was after Borh's answer to Einstein at the 1930 Solvay conference that the Bohr-Einstein debates went in that direction.

 

is he getting into string theory?

However picturesque the notion that everything is made of strings vibrating in 10 dimensions sounds, the classical action must be quantized just like in any other quantum field theory. String theory does not solve the mystery of what that means; it takes it for granted.

Edited April 2, 2012 by Creation

[Ya Mu]

Creation, Creation, Creation; you are really good at explaining this. Please continue.

[Taomeow]

http://books.google....id=T6fWst-KdoYC

 

ai yeah geometry still trumps physics/quntuam physics

 

 

[Birch]

What's that that Jesus has got his compass on? Looks like a cell or something.

[Creation]

OK, geometry it is!

 

I will mark with a (!) places that I recommend drawing a picture or doing a little pondering.

 

What does it mean for a surface to be curved? From a 3rd dimensional vantage point it is easy: you look at it, and basically just know. Mathematically, you look at the tangent planes. The tangent plane of a surface at a point is the plane that, at least nearby that point, touches the surface only at that point.

If the tangent planes are not parallel to each other, the space is curved. Like, say, on a sphere, the tangent plane at the north pole will be perpendicular to a tangent plane of a point on the equator (!).

 

OK, but what if the surface is actually very thin and hollow on the inside and there is a bug crawling around in there. As far as that bug is concerned, there are only 2 dimensions, that is, there is only forward backward left and right, no up or down. What does curvature mean now?

 

Mathematically, this is called studying a surface intrinsically. You treat the surface as it's own independent thing, not as something embedded in a larger 3 dimensional Euclidean space. So what is an intrinsic notion of curvature, i.e. how can the ant know whether or not the surface it is crawling in is curved or not?

 

Well first, what is a tangent plane at a point, intrinsically speaking? It is the space of all the "velocity vectors" an ant can have at that point (!). (A vector is a quantity with both magnitude and direction, a velocity vector is therefore a direction and a speed, a "bearing" if you will).

 

The next piece of the curvature puzzle is called "parallel transport".

 

In Euclidean (i.e. flat) space, if you have a vector at one point, you can slide it to any other point without turning or stretching it. Actually, you can slide it along any path from one point to another, not just along a straight line (!).

 

Now, suppose our ant is traveling down the 0 degrees longitude meridian, and we decide to take the tangent vector at the north pole pointing in the direction the ant is traveling and slide it down along with the ant. Now it is no longer tangent to the sphere, in fact it is completely perpendicular to it! (!) Actually, as soon as you slid the vector just a tiny bit along that meridian it was already not tangent to the sphere any more. So as far as our ant is concerned, we are not actually doing it right. What we need to do is instead of just sliding the vector along, we also need to rotate it a bit with each step to keep it tangent to the sphere. This way it always points in the same direction the ant is going. It sort of "rolls" with the sphere. But from the ant's perspective, nothing is being rotated because there is only the sphere. It is only from the 3-D perspective that something is being rotated. This keeping the vector tangent to the sphere is called parallel transport. By the way, just to get a feel for the concept, notice that if we had started with a vector perpendicular to the ant's direction of motion and rotated it a bit with each step to keep it tangent to the sphere, it would have stayed perpendicular to the ant (!).

 

But you don't need to have the surface embedded in 3 dimensions to get a notion of parallel transport. You can just specify some data on the surface itself that tells you how to parallel transport vectors in an intrinsic way. Mathematicians call this data the connection, because it connects the different tangent spaces together.

 

It is the connection that tells you what the analog of a straight line will be in an arbitrarily curved space. If the ant "follow it's nose" so to speak, without turning left or right, it's velocity vector is the parallel transport of itself (!). A curve whose velocity vectors are parallel transports of themselves is called a geodesic. In flat space, these are the straight lines (!). On a sphere, they are the circles of maximal diameter.

 

OK, one more step to an intrinsic notion of curvature. Notice that parallel transport in flat space, aka sliding, has the property that if you transport/slide a vector along two different paths between the same two points, you end up with the same answer (!). But again consider the tangent vector at the north pole of the sphere pointing at the 0 degrees longitude meridian. If you parallel transport it down the meridian until you hit the equator, it will be pointing South. But if you first parallel transport it along the 90 degrees East meridian line until it hits the equator, and then parallel transport it along the equator until you hit 0 degrees longitude, it will be pointing West (!).

 

It is this property of parallel transporting a vector along two different paths and getting two different answers that mathematicians call "intrinsic curvature".

 

Next up is to relate all of this to physics, gravity in particular. For now, just notice that if we can talk about a 2 dimensional curved space "intrinsically", i.e. as it's own thing without a notion of a 3rd dimension it is curving in, we can do the same in any number of dimensions. Like say, 4.

Edited April 3, 2012 by Creation

[Apech]

What's that that Jesus has got his compass on? Looks like a cell or something.

 

Pizza.

[zerostao]

are you suggesting that " gravity in particular " is geometry?

[Creation]

are you suggesting that " gravity in particular " is geometry?

I have not suggested this. For one, I am wary of using the word "is" in such a cavalier way. Secondly, a good story teller does not give away the ending, but rather hints at it.

 

So for now all I'll say is that gravity can be related to geometry using the idea of a connection.

Edited April 3, 2012 by Creation