First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)

[Alex K]

That's not an easy question. I'll try to do the following - present several different aspects of it separately in the hopes of providing a clearer picture.

Maybe the cleanest approach is via Emmy Noether's theorem on conserved quantities. It states that any continuous symmetry in the laws of nature gives rise to a conserved physical quantity, and that vice versa this quantity determines how to perform the symmetry operation.

The relevant case for us is that the laws of nature do not seem to change over time, at least to a very good approximation. This means that formally moving back and forth in time is a symmetry of the laws of nature, just as rotation is a symmetry of a sphere. Noether's theorem states that there should be a conserved quantity associated with this symmetry. We call this quantity "Energy". The theorem makes sure that Energy is not lost over time and therefore Energy appears to us as if it were a substance flowing through space - if it is not lost in total, the reduction of energy in one place must correspond to the increase of energy elsewhere, in the case of the known laws of nature, neighboring patches of space (continuity equation). This creates the notion of a flow. Vice versa, by the same theorem, knowing the Energy of every configuration of particles and forces is sufficient to know what happens as time progresses, to know the dynamics.

[Sappho]

That's not an easy question. I'll try to do the following - present several different aspects of it separately in the hopes of providing a clearer picture.

Maybe the cleanest approach is via Emmy Noether's theorem on conserved quantities. It states that any continuous symmetry in the laws of nature gives rise to a conserved physical quantity, and that vice versa this quantity determines how to perform the symmetry operation.

The relevant case for us is that the laws of nature do not seem to change over time, at least to a very good approximation. This means that formally moving back and forth in time is a symmetry of the laws of nature, just as rotation is a symmetry of a sphere. Noether's theorem states that there should be a conserved quantity associated with this symmetry. We call this quantity "Energy". The theorem makes sure that Energy is not lost over time and therefore Energy appears to us as if it were a substance flowing through space - if it is not lost in total, the reduction of energy in one place must correspond to the increase of energy elsewhere, in the case of the known laws of nature, neighboring patches of space (continuity equation). This creates the notion of a flow. Vice versa, by the same theorem, knowing the Energy of every configuration of particles and forces is sufficient to know what happens as time progresses, to know the dynamics.

Thank you. Although it's hard for me to read this kind of things in english, I think I understand it.

If you don't mind, I have another question, but this is probably an easier one: 
When I think about it myself, it seems reasonable that every elementairy particle is one-dimensional, since only a point is not divisible.
Yet in other sources I read that it must be presented as a function of where it will appear, and those functions can even collide(?) (Bose-Einstein condensate).
Are they both correct, or is my reasoning as usual incorrect?

[Alex K]

@Sappho, which language would you prefer? I can offer German or really really bad Spanish or French

So, those particles we call elementary particles (*) are usually considered to be pointlike (apart from advanced speculative ideas like string theory), because there is no experimental indication that they are not, at the scales we have tested experimentally - this means they are treated as zero-dimensional in space, and one-dimensional in spacetime ("world lines"). In particular, they are treated as point particles in the Standard Model.

Now, these pointlike particles have a quantum uncertainty in their location, which at each point in time is expressed by a wave function

f(x)



Here, x is the putative location, and f(x) squared is the probability to find the particle at position x, roughly speaking. So, the quantum uncertainty is spread out over three dimensions, but we are talking about the uncertainty of one location parameter, and therefore one still talks about it being a point particle. Is that somewhat clear?

An example of a non-pointlike thing: In contrast to the above, the quantum wave function of a string must assign a probability not only to each possible overall location of the string, but to all possible combinations of locations of each piece of the string, i.e. its shape and size. You then get a much more complicated object which is a 1-dimensional thing in space, the shape, size *and* position of which have quantum uncertainty.


(*) It may well turn out that today's elementary particles are not elementary if one looks more closely, i.e. with more energy, i.e. with a bigger collider.

[Sappho]

@Sappho, which language would you prefer? I can offer German or really really bad Spanish or French

So, those particles we call elementary particles (*) are usually considered to be pointlike (apart from advanced speculative ideas like string theory), because there is no experimental indication that they are not, at the scales we have tested experimentally - this means they are treated as zero-dimensional in space, and one-dimensional in spacetime ("world lines"). In particular, they are treated as point particles in the Standard Model.

Now, these pointlike particles have a quantum uncertainty in their location, which at each point in time is expressed by a wave function

f(x)



Here, x is the putative location, and f(x) squared is the probability to find the particle at position x, roughly speaking. So, the quantum uncertainty is spread out over three dimensions, but we are talking about the uncertainty of one location parameter, and therefore one still talks about it being a point particle. Is that somewhat clear?

An example of a non-pointlike thing: In contrast to the above, the quantum wave function of a string must assign a probability not only to each possible overall location of the string, but to all possible combinations of locations of each piece of the string, i.e. its shape and size. You then get a much more complicated object which is a 1-dimensional thing in space, the shape, size *and* position of which have quantum uncertainty.


(*) It may well turn out that today's elementary particles are not elementary if one looks more closely, i.e. with more energy, i.e. with a bigger collider.

Thank you, it is indeed a more clear for me.

As for the languages, I think English is the best option since the only language which would work better is Dutch. My german and french are not capable of bearing this matter

I hope I'm not boring you since I have yet another question, of which I will never run out as long as I live
Forces. I do not really understand how it's information is exchanged.
For example: the gravitational field of the earth, in theory, is present in the entire universe. Now the earth explodes, yet at the exact same moment that change can be felt everywhere (or not?). The information about that is transmitted by gravitons, and therefore it would mean that they would travel at in infinite speed and there would be an infinite amount of them, since the field is present in every point in space, which would mean there are infinite particles in the universe.
Obviously this is wrong, but I can't find the mistake(s).

[vorlon13]

To the extent possible to date, all tests on electrons have revealed them to be 'absolutely' point like.

It's an amazing thought something demonstrably exists with no internal volume. At all.

How can that work ??

[Alex K]

@Sappho

Gravity waves, and their hypothetical quanta, the gravitons, move at the speed of light!

@Vorlon
Absolutely is a bad word choice. Pointlike within resolution of current experiments.
I have no definite answer, but it seems likely that at some scale, this pointlikyness is replaced by something else, such as a string. One indication for that is that the pointyness of particles leads to infinities in the theory which one has to remove with a mathematical trick. That could be a hint that pointlikeness, fundamentally, is BS.

[Sappho]

@Sappho

Gravity waves, and their hypothetical quanta, the gravitons, move at the speed of light!

@Vorlon
Absolutely is a bad word choice. Pointlike within resolution of current experiments.
I have no definite answer, but it seems likely that at some scale, this pointlikyness is replaced by something else, such as a string. One indication for that is that the pointyness of particles leads to infinities in the theory which one has to remove with a mathematical trick. That could be a hint that pointlikeness, fundamentally, is BS.

So they move at the speed of light (because they have no mass?) but then how come the field can be felt immediatly? Or can it not?
For example if the sun would suddenly vanish, would the earth immediatly fly away or would it take as long as light would travel from the sun to the earth?

[Alex K]

It can not be felt immediately! If the sun disappeared, earth would stay on its course for 8 mins.

[vorlon13]

. . .to the extent possible . . . absolutely pointlike . . .


Um, I think I said it right with the noted qualifier. It's also my understanding that as the machinery has improved over the decades, the size of the electron remains 'zero' within the measurement error. We aren't even seeing a 'hint' our machinery is even getting close to delineating a size.



IIRC, 'pointlike' these days means <10^-43 meter. For beings in the size range of 10^-400 meters, an electron would be bigger than our universe appears to us.

[Alex K]

Maybe, but then again, since the planck scale is larger than that, the notion of size breaks down in this regime.