Particles - higgs boson

[Seze Mune]

It may well be beyond the ability of the human mind to understand Reality in the
truest operational sense.

[Clarke]

There certainly have been more bizarre ideas postulated. Apparently, there is an idea that is popular where the universe as we know it is some sort of 3D projection from a kind of holographic 2D plane. That is kind of a challenge to wrap your head around.

One theory I do strongly question though, is the whole idea of multiverses. Especially multiverses that intersect, kind of like what you are suggesting. I think there are enough oddities in our own universe to explain without postualting that there could be other universes.

A continuously varying multiverse is the quickest and "simplest" way to explain the results of conventional quantum mechanics, though.

[`Eylan Ayfalulukanä]

Txantsan, ma Clarke! Great to see you here. I will never forget the quality time we were able to spend together at AvatarMeet, discussing physics and all manner of other interesting subjects, until I was unable to stay awake! It is not often I run into folks that can discuss these subjects and know what they are talking about. I am really hoping that our talk at AvatarMeet will not be our last!

In any case, what you are saying about multiverses is new for me. You might want to explain how the existence of a multiverse solves some of the problems of quantum mechanics.

[Clarke]

If you build the phase space of all configurations of the universe, then you can model the result of a measurement as two different paths in this "space". However, since the probability function of e.g. an electron's position is continuous, not discrete, there is technically an infinite amount of places an electron can potentially end up. Because of that, there is an infinite number of paths into the future, each where the electron ended up somewhere slightly different.

This has a really neat explanation for things like quantum entanglement: when two things are entangled, no spooky-action-at-a-distance is needed. Instead, when the two objects are entangled, the phase space is changed so the configurations where the particles are not entangled don't happen.

It also readily explains the totalitarian principle: because there are an infinite number of paths from now until then, some of which involve strange things happening, you've got to take all of them into account to get the right answer.

[`Eylan Ayfalulukanä]

Very interesting!

But let's say we start out with an electron at a known position in the orbital of an atom. The electron is orbiting at ground state. Provided that there are no inputs or outputs of energy to that atom, the electron will follow the orbit described by the orbital. The uncertainty principle tells us that we cannot be exactly sure where the electron will be on that orbital at T+ some arbitrary amount. However, we can be reasonably certain it has moved.

We can measure T+ arbitrary interval to a high degree of accuracy. And for all intents and purposes, time only moves forward. So, at T+arb , the electron is in a different position, but not one we are exactly sure of (but almost certainly lies along the orbital). But regardless of where the electron is, exactly the arbitrary amount of time has elapsed. Thus, there is only one future, but an infinite number of positions the electron could occupy at that time. However, the electron occupies exactly one position at that time.

For another observer, this could be their frame of reference as to the resting place of the electron. (But could you then measure the difference between the frames of reference, and then determine the exact position of the electron at T+arb?)

So although the position of the electron cannot be determined with certainty, the time can. So, there is no implication of multiple universes, because the electron is still there, and has for the most part, moved predictably.

I think the Heisenberg uncertainty principle is one of the most misunderstood and abused scientific principles (along with evolution) there is. Although it adds a lot of 'strangeness' to quantum physics, the principle by itself is not strange.

[Seze Mune]

Very interesting!

But let's say we start out with an electron at a known position in the orbital of an atom. The electron is orbiting at ground state. Provided that there are no inputs or outputs of energy to that atom, the electron will follow the orbit described by the orbital. The uncertainty principle tells us that we cannot be exactly sure where the electron will be on that orbital at T+ some arbitrary amount. However, we can be reasonably certain it has moved.

We can measure T+ arbitrary interval to a high degree of accuracy. And for all intents and purposes, time only moves forward. So, at T+arb , the electron is in a different position, but not one we are exactly sure of (but almost certainly lies along the orbital). But regardless of where the electron is, exactly the arbitrary amount of time has elapsed. Thus, there is only one future, but an infinite number of positions the electron could occupy at that time. However, the electron occupies exactly one position at that time.

Why would there not be an infinite number of futures? If you posit an infinite number of positions the electron could occupy at one time, then those infinite positions are all as real or as unreal as any other one.  When you decide to measure the electron, you've collapsed it at one point along one trajectory, but how can you say with any certainly that there aren't any number of probable yous taking measurements along the other trajectories at the "same time" as the you, you believe yourself to be? And even then, from that point forward, there are any number of OTHER positions the electron could be in at some time in the 'future', so there really ISN'T any one particular future.  There is only the 'now' which is really unending action anyway.

For another observer, this could be their frame of reference as to the resting place of the electron. (But could you then measure the difference between the frames of reference, and then determine the exact position of the electron at T+arb?)

So although the position of the electron cannot be determined with certainty, the time can. So, there is no implication of multiple universes, because the electron is still there, and has for the most part, moved predictably.

I think the Heisenberg uncertainty principle is one of the most misunderstood and abused scientific principles (along with evolution) there is. Although it adds a lot of 'strangeness' to quantum physics, the principle by itself is not strange.

I'm not so sure about that, but then again I've fairly permeable with respect to hard scientific assumptions.

[Clarke]

However, the electron occupies exactly one position at that time.

This is classical thinking in a quantum context. It doesn't work. 

[`Eylan Ayfalulukanä]

However, the electron occupies exactly one position at that time.

This is classical thinking in a quantum context. It doesn't work. 

Here's a chance to educate me. Does this make sense?
From what I understand of the uncertanty principle is, if you know a particle's position, you don't know its velocity. if you know a particle's velocity, you can't know its position. But to an observer in a single frame of reference, who knew a particle's position at time zero, that particle will be in a new position. Since we are dealing with a single particle, there can be only one position that this particle now occupies at T+arb, even if we cannot predict what this position will be.

[Seze Mune]

However, the electron occupies exactly one position at that time.

This is classical thinking in a quantum context. It doesn't work.  

Here's a chance to educate me. Does this make sense?
From what I understand of the uncertanty principle is, if you know a particle's position, you don't know its velocity. if you know a particle's velocity, you can't know its position. But to an observer in a single frame of reference, who knew a particle's position at time zero, that particle will be in a new position. Since we are dealing with a single particle, there can be only one position that this particle now occupies at T+arb, even if we cannot predict what this position will be.

Hmm.  Forgive my lack of scientific acumen, but I want to understand this, so......I would say that it is probably incorrect to assume from a quantum perspective that there is only one position that this particle now occupies at T+arb because you don't know what other events may have intersected with that electron between time zero and T + arb.  Therefore there are ∞ number of probable events which will have intersected, causing ∞ number of probable positions, none of which will be considered 'real' events or positions until they are 'collapsed' at the point of measurement. Which to my limited mind makes the whole thing moot.

Or am I just hopelessly confused?  

[`Eylan Ayfalulukanä]

Kehe, ma Seze, I don't think you are confused. You are very close to the right thinking.

Although there is no way to accurately PREDICT where the particle will be at T+arb, the particle is IN FACT in just one spot. You are right about 'collapsing all the measurement errors' in finding where the particle ACTUALLY is.

So, given that a particle can only be in one spot at T+arb, is it safe to assume that this is the only spot it could occupy, given the infinite possible places it could occupy, when all possible forces acting on the particle have been properly summed? Is the uncertantity of uncertantity derived from the fact that it is impossible to measure all those forces with sufficient accuracy to determine where the particle could be? Are our abilities to measure particle positions improving such that we can limit the possible positions of the particle at T+arb to a reasonable subset?

[Clarke]

However, the electron occupies exactly one position at that time.

This is classical thinking in a quantum context. It doesn't work.  

Here's a chance to educate me. Does this make sense?
From what I understand of the uncertanty principle is, if you know a particle's position, you don't know its velocity. if you know a particle's velocity, you can't know its position. But to an observer in a single frame of reference, who knew a particle's position at time zero, that particle will be in a new position. Since we are dealing with a single particle, there can be only one position that this particle now occupies at T+arb, even if we cannot predict what this position will be.

Unfortunately, I don't really have time or energy ATM to write up an explanation of precisely what's going on. However, have a look at the double-slit experiment, and try and explain to me how you can make it work if the electron has a definite, though indeterminate, place to be.

[Tsanten Eywa 'eveng]

The Higgs Boson may cause the end of the universe. Scientists in Geneva have calculated, and it tells that the universe, will come to an end in about tens of billions of years, because of the Higgs Boson.

The mass of the particle, which was uncovered at the world's largest particle accelerator — the Large Hadron Collider (LHC) in Geneva — is a key ingredient in a calculation that portends the future of space and time.
"This calculation tells you that many tens of billions of years from now there'll be a catastrophe," Joseph Lykken, a theoretical physicist at the Fermi National Accelerator Laboratory in Batavia, Ill., said Monday (Feb. 18) here at the annual meeting of the American Association for the Advancement of Science.
"It may be the universe we live in is inherently unstable, and at some point billions of years from now it's all going to get wiped out," added Lykken, a collaborator on one of the LHC's experiments.

http://www.space.com/19850-higgs-boson-universe-future.html

[Vawmataw]

The Higgs Boson may cause the end of the universe. Scientists in Geneva have calculated, and it tells that the universe, will come to an end in about tens of billions of years, because of the Higgs Boson.

The mass of the particle, which was uncovered at the world's largest particle accelerator — the Large Hadron Collider (LHC) in Geneva — is a key ingredient in a calculation that portends the future of space and time.
"This calculation tells you that many tens of billions of years from now there'll be a catastrophe," Joseph Lykken, a theoretical physicist at the Fermi National Accelerator Laboratory in Batavia, Ill., said Monday (Feb. 18) here at the annual meeting of the American Association for the Advancement of Science.
"It may be the universe we live in is inherently unstable, and at some point billions of years from now it's all going to get wiped out," added Lykken, a collaborator on one of the LHC's experiments.

http://www.space.com/19850-higgs-boson-universe-future.html

Hmm... A good theory.

Hopefully the humanity will no longer exist when it will happen... if it's 100% true.

[Tìtstewan]

An interesting theory!
It interesting when people talking about posibillities of death of universe.

[`Eylan Ayfalulukanä]

I have always speculated that there must be some sort of connection between the Higgs field and dark energy.

The Higgs field, to do what it does, has to permeate the universe. Although we can (barely!) detect its associated gauge boson (the Higgs boson), we only know about the Higgs field by its effect on other particles (it gives them mass). So, if something about this field changes as the universe expands and ages, it will lead to one of the proposed theories (I personally lean towards 'the big rip'). I also think the Higgs field has something to do with 'vacuum energy'. Slä awnga zene nivume  nìtxan!

There are a number of things we know about that rest right along a line that separates stable from unstable. (the cosmological constant, the fine structure constant, etc.) Tiny deviations from this line control what will happen. And most of these deviations are right at (or beyond) what we can accurately measure.

But I am not going to worry. The matter in my body will be well-dispersed (along with the rest of the earth) long before any of this becomes practically relevant.

[Clarke]

Here's a chance to educate me. Does this make sense?
From what I understand of the uncertanty principle is, if you know a particle's position, you don't know its velocity. if you know a particle's velocity, you can't know its position. But to an observer in a single frame of reference, who knew a particle's position at time zero, that particle will be in a new position. Since we are dealing with a single particle, there can be only one position that this particle now occupies at T+arb, even if we cannot predict what this position will be.

I don't have anything better to do at the moment, so have an explanation!

In quantum mechanics, the position and momentum of a particle are represented by waves. Now, let's quickly brush a lot of complexity under the rug, and say that we have a particle confined to a bounded 1D line (i.e. it has defined ends) in space. The particle can be anywhere on this line, but it can only be on the line. We can then represent the chances of finding the particle at a particular position by a single value between 0 and 1, and when we string all these values together, we get a wavy line. (It's wavy because the particle's more likely to be found in some places than others.)

Now, remember the really annoying functions from high school, sin and cos? It turns out that by combining lots and lots of sin waves with different amplitudes and frequencies, it is possible to produce any continuous repeating curve, even what we'd think of as non-curvy ones, like sawtooth waves. (That page even provides the formula for doing so) This means that, no matter how convoluted our wavy line representing the particle's position is, it is equal to some combination of sine waves added together. Remember that last sentence - it will be important later.

Enter the Fourier transform! The FT is a slightly weird thing - it is a mapping that takes one function, such as our wavy line from above (which, if you think about it, could be expressed a relationship between the height and distance sideways) and produces an entirely separate function, i.e. another curve. This new curve has a curious property - if the curve we feed in originally is a combination of sine waves, the curve we get out has peaks representing the frequencies of those sine waves. For a good illustration of this, look at the first and fourth pictures here. You can also imagine the displays on lots of music players that show the bass/treble frequencies in the music being played - the player is doing a FT to get that information.

What does this have to do with particles moving around? This is the clever bit - the momentum of a particle can also be expressed as a wave, as we did above with the position. We also find that these two waves are related - the momentum wave is the Fourier transform of the position wave!

What we were originally thinking about was what would happen if we knew the particle's position very accurately. That is, our "wave" representing the particle's chances of being somewhere on our line has a very tall peak, and falls off to 0 either side of the peak very quickly - it is very likely to be in that one place, and not likely to be anywhere else. We wish to find what the corresponding wavy line for the momentum looks like, and to do that, we need to know how to build the very tall peak out of sine waves. It must be possible to do, because we know that, somehow, we can do it with any continuous curve, and this is definitely continuous.

The problem almost arises when we work out the answer - to build our thin peak, we need to add together a large number of sine waves in equal proportions to one another. If we somehow knew the position infinitely accurately, we would need an infinite numbers of sines. This isn't, itself, the problem, since there's nothing illogical about adding together infinitely many functions like this. The problem arises when we take the Fourier transform of this (infinitely thin) tall peak - the transform works, and produces a function which reflects the fact that there were infinitely many equally spaced peaks in the original function. That is, it returns a "wave" that is an almost, if not absolutely, flat line.

Let us return from the abstract maths to the land of physics and consider what that means: it means that our particle is equally likely to have any possible momentum value, from 0 to ludicrous speed in either direction. (We are still working in 1 dimension at the moment, for simplicity.)

So let's let the universe tick for an instant. Now, our particle has moved. We knew where it was a moment ago, but now we face a challenge: we could pick any point on the line the particle is restricted to, and then calculate how far away this point is from where we knew the particle was. The line is only finitely long, so this will always be a finite distance. Because it is a finite distance, there will be some finite value for the particle's momentum that will take it between the two places in the one tick of the clock we have let the universe experience.

We established earlier that the particle could potentially have any possible momentum value and thus in turn could be anywhere in the line we have reserved for it, even after only a single tick. After one tick, the particle is completely lost. Q.E.D.  

[`Eylan Ayfalulukanä]

Ma Clarke, very interesting!

I am not sure I agree with your reasoning.

If you take the FT of a arbitrarily varying wave, you will get a series of peaks in the resulting graph that vary in height depending on the amplitude of the sine waves needed to build that curve. These peaks will not necessarily be in an orderly array, and the more irregular the original wave is, the more irregular the FT will be.

But if the wave function is a pure sine wave, you will get one and only one peak that has a peak value of unity (in relation to the amplitude of the wave), and theoretically infinitely thin. Such a peak will determine the position of the particle with certaintity.

Now, I don't know if you are getting your flat line by doing a forward FT on the peak graph, or an inverse FT. An inverse FT of such a peak will give you a very nice sine wave. If the position of the peak on the X axis of the graph is known, then one can, from its position, deduce the frequency of the resulting since wave (and vice versa). If we know the frequency (or its inverse, wavelength), and how long our arbitrary time period is, we can determine with a fair degree of accuracy where the particle will be. If the wave function of the particle is anything but a pure sine wave, predicting the particle's position becomes much harder. Very few natural functions are pure sine waves, so as a result, the position of the particle at T+1 cannot be exactly pinned down.

But regardless of where the particle moved to, if we can accurately measure its position at T+1, it allows us to reconstruct everything that happened to the particle between T and T+1 (again assuming it behaved in a linear manner). This will also give us an idea where the particle has moved to at T+2 (Provided other smaller variables have been taken into account as well).

Fourier transforms are the basis of the most common types of digital video compression, and are designed to relate time varying events to frequency. Once the frequency data in a small area of pixels in an image has been extracted, the amplitudes of some of the resulting signal 'peaks' are  further analysed, and if needed adjusted to create the right amount of compression. This particular FT variant is called a 'Discrete Cosine transform', or simply, DCT. It is 2 dimensional. If no signal peaks are altered, the DCT is exactly reversed by the inverse DCT, and the original signal is recovered.

One of the few places outside of physics that complex number are used is AC electronics. The impedance of a circuit consists of two values, drawn at right angles to each other, like the sides of a right triangle. If these sides are in line with a graph, the X axis side represents the resistance of the circuit element. The Y axis side represents the reactance of the circuit element. If the Y axis side is above the X axis side, the reactance is said to be inductive. If the Y axis side is below the X axis side, the reactance is said to be capacitive. The length of the hypotenuse is the impedance of the circuit element. The cosine of the angle between the X axis side and the hypotenuse is called the power factor. Now, for instance, the input to a transmission line feeding an antenna is often designed to be 50 ohms, purely resistive. Under these conditions, the reactance is zero, the power factor is unity, and the resistance is equal to the impedance. And maximum power transfer takes place if the transmitter's (the 'generator') source impedance is also 50 ohms resistive. However, perfect antennas or transmission lines are rarely encountered, and the impedance will usually be something other than 50 ohms. But if this impedance is measured at say, 53 ohms, this tells one very little about the reactance, or how to correct it. Is the resistive part or the reactive part causing the impedance to be other then 50 ohms? (The reactive portion of the impedance is usually undesirable, but can be cancelled out with an equal but opposite sign reactance.) So, it is very common to use a complex number to indicate impedance in an AC circuit. The resistance is the 'real' part, and the reactance is the 'imaginary' part. Reactance is 'imaginary' because in a perfect circuit, all of the energy consumed in exciting the reactance is later returned to the generator, and it average energy level is zero, regardless of the size of the reactive component. But even though the average value is zero, the instantaneous value of this energy either has to be supplied or absorbed, and this happens 'out of phase' with the resistive energy. This creates much extra work for the generator, and it is therefore undesirable.  So, if we measure 53 ohms impedance at the input to our transmission line, and know the reactive part is capacitive, and the resistive part is 50 ohms, we can easily determine the reactance is -17.57 ohms, the sign indicating the reactance is capacitive. This can be conveniently expressed as the impedance is 50-j17.57 ohms. If the reactance were inductive, it would be 50+j17.57 ohms. Now, in designing impedance correction networks, this notation makes designing the necessary circuit to cancel out the reactive part of an impedance, and match the resistive part to the value of the generator, much easier. Under this condition, the most power is transferred, and the generator is 'happy'. This condition is also known as 'impedance matched'.

In any case, thanks for the post. I needed something intellectually stimulating this evening!

[Clarke]

Now, I don't know if you are getting your flat line by doing a forward FT on the peak graph, or an inverse FT. An inverse FT of such a peak will give you a very nice sine wave.

I am doing a forward FT on the peak. Though, technically, what I was doing was a absolute-square of the FT of the peak, since the FT of a peak is actually a combination of real and imaginary sine waves overlapping each other.

If the position of the peak on the X axis of the graph is known, then one can, from its position, deduce the frequency of the resulting since wave (and vice versa). If we know the frequency (or its inverse, wavelength), and how long our arbitrary time period is, we can determine with a fair degree of accuracy where the particle will be. If the wave function of the particle is anything but a pure sine wave, predicting the particle's position becomes much harder. Very few natural functions are pure sine waves, so as a result, the position of the particle at T+1 cannot be exactly pinned down.

Remember, the sine wave represents probability of momentum, not position. We can imagine we have a function called P(m), which represents the probability of the particle having the momentum m. That means that, for a given m, chances are, the particle will have moved P(m)*m (e.g. if it has a 10% chance to move 5 units, we treat that as it moving 0.5 units "on average"...) so to get the actual average, taking into account all the different values of m it could have, we need to integrate P(m)*m with respect to m. (Since that gives us what happens when you add up the infinitely many m)

Unfortunately, it could have any real value of m, so we need to integrate across an infinite line, and this integral doesn't converge, and so the particle has no defined "average" position after the next step. 

(I'm still using the simplified real numbers above, because I'm too busy to do the calculation in complex numbers right now.)

But regardless of where the particle moved to, if we can accurately measure its position at T+1, it allows us to reconstruct everything that happened to the particle between T and T+1

I was assuming, for the sake of simplicity, that time is discrete and comes in chunks of "1" (However long that is)

(again assuming it behaved in a linear manner)

I think the best metaphor would be that this is like assuming that the Na'vi will buy your jeans and light beer.

This will also give us an idea where the particle has moved to at T+2 (Provided other smaller variables have been taken into account as well).

What smaller variables might those be?