Length Contraction of Protons in the LHC

[Neil Marshall]

What affect does the phenomenon of "length contraction" have on the shape (e.g. spherical, rugby ball, barbell, donut) of protons accelerated to 0.999999991 c in the LHC?

 

[berkeman]

What affect does the phenomenon of "length contraction" have on the shape (e.g. spherical, rugby ball, barbell, donut) of protons accelerated to 0.999999991 c in the LHC?

Welcome to the PF

Interesting question. Is this a schoolwork/homework question?

 

[mathman]

Flat disc?

 

[Cryo]

In which reference frame? If not the rest frame, then how would you measure it.

 

[Neil Marshall]

Welcome to the PF

Interesting question. Is this a schoolwork/homework question?

No this is not a schoolwork/homework question. I'm a 72 year old nerd who loves physics.

 

[Neil Marshall]

Flat disc?

Mathman,
Possibility. I've heard tell that photons are 2 dimensional discs experiencing neither time or distance. Unfortunately, that implies that the proton becomes mass-less. Thanks for the feedback.
Neil

 

[Neil Marshall]

In which reference frame? If not the rest frame, then how would you measure it.

Cryo,

Great question. It's a way of asking the question "is length contraction real or just an observation which is IRF dependent. I think the jury is still out on that question. Personally, I fall on the reality side, but let me insert a snippet from the Wikipedia article on "length contraction".

https://en.wikipedia.org/wiki/Length_contraction

"Heavy ions that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light. And in fact, the results obtained from particle collisions can only be explained when the increased nucleon density due to length contraction is considered".[14][15][16] [14] Brookhaven National Laboratory. http://www.bnl.gov/rhic/physics.asp. [15] Manuel Calderon de la Barca Sanchez. "Relativistic heavy ion collisions". [16] Hands, Simon (2001). "The phase diagram of QCD". Contemporary Physics. 42 (4): 209–225. arXiv:physics/0105022 

. Bibcode:2001ConPh..42..209H. doi:10.1080/00107510110063843.

I know that Wikipedia is not a blue-ribbon source and I'd like to chat with someone at CERN about this issue. If you know anyone from CERN who might be willing to chat, please let me know.

Thanks for the feedback,
Neil

 

[mfb]

Mathman,
Possibility. I've heard tell that photons are 2 dimensional discs experiencing neither time or distance. Unfortunately, that implies that the proton becomes mass-less. Thanks for the feedback.
Neil

Photons don't have a shape.

Protons, as everything, get length contracted as seen in the lab frame. As they don't have an actual three-dimensional structure anyway this is nothing you could see.

 

[Cryo]

Cryo,

Great question. It's a way of asking the question "is length contraction real or just an observation which is IRF dependent. I think the jury is still out on that question. Personally, I fall on the reality side, but let me insert a snippet from the Wikipedia article on "length contraction".

Neil

This is actually a very subtle topic which I would like to get some time to understand, but currently I don't. What I can do is provide you the reference I intend to study when I do get the time :-) (http://iopscience.iop.org/article/10.1070/PU1975v018n08ABEH004917/meta)

Basically, the question whether length contraction is real or artefact of breaking the spacetime into space and time is sort of moot if we only consider constant velocities. However, if we consider the case when an object starts at rest, then accelerates, and then reaches a constant velocity, the question becomes interesting. If length contraction is real, does one have to put extra energy to actually contract the object (i.e. bring atoms closer together etc)? Of course, there is no magic there. Electromagnetism is fully compatible with special relativity, so there is no surprise you get length contraction. But can you "see" it in dynamics of the system (theoretically)? This is what the paper is about (I believe)

 

[vanhees71]

Photons don't have a shape.

Protons, as everything, get length contracted as seen in the lab frame. As they don't have an actual three-dimensional structure anyway this is nothing you could see.

Photons don't get length contracted since, as you correctly stated, they have no shape, at least not in the usual common sense of the word. A photon is a single-particle Fock state. The common example is the generalized eigenvector of momentum and helicity $|\vec{p},\lambda$.

A Lorentz-boosted photon is a state with the correspondingly changed momentum (describing the Doppler shift due to relative motion between photon source and observer) and the same helicity (since helicities are independent of the reference frame).

 

[mathman]

Mathman,
Possibility. I've heard tell that photons are 2 dimensional discs experiencing neither time or distance. Unfortunately, that implies that the proton becomes mass-less. Thanks for the feedback.
Neil

They would be flat in the rest system, but unchanged in their own inertial system, so they would not be mass-less. In the rest system they are quite heavy.

 

[Neil Marshall]

To mfb, cryo, vanhees71, and mathman,
Thank you all very much for responding to my questions. I'm a physics novice but rabid enthusiast. I would like to respond to each of you in this posting.

mfb: You say that protons have no shape. I interpret this to mean they don't have any nominal shape, but not that they have no shape at all. If you mean that protons do not have any shape(s) at all, then that seems illogical to me. Protons consist of two up-quarks and one down quark. I've read that the radius of a proton is 8.3E-16 meters. I've also read that quarks have current mass (i.e. down=2.00E00 MeV, up=4.80E+00 MeV) and constituent mass (down=3.40E+02 MeV and up=3.36E+02 MeV). If protons have a radius and quarks have mass, and the Pauli exclusion prevents the quarks from occupying the same state would you please explain to me why protons don't occupy a volume of spacetime (i.e shape)?

cryo: Thank you for the reference article on time dilation and length contraction. I will read it thoroughly and respond in my next posting. Until then, the problem I'm working on with a colleague is " what happens to the shape of a proton when it is accelerated to .9999999991 the speed of light (i.e. in the LHC) which you pointed out in your response. You're right, the question is can you "see" it in internal dynamics of the proton (theoretically)?

vanhees71: Thank you very much for your response. You introduced me to an area of research that I would not otherwise have considered. Although your response focused on photons, it introduced me to the concept of helicity. This may prove useful to my colleague and I in our analysis of accelerated proton shape(s).

mathman: I'm not sure I understand your statement that protons would be flat in the rest system. Could you elaborate on that? I'm not sure what you mean by flat?

 

[mfb]

I said photons have no shape. Photons and protons are completely different things, despite the similar name. In the quoted part you asked about photons.

Protons are spherical, but they don't have a three-dimensional internal structure. You can't say "this quark is here and that is there".

 

[Anashim]

What can possibly explain the increase of both their elastic and inelastic total cross-sections as the C.O.M. energy increases?

This question could be off-topic, but I am not quite sure.

In:

https://arxiv.org/abs/1807.06471

They claim that the black disk limit has been exceeded. That means that over 50% of the $pp$ collisions are purely elastic (which can arguably be labelled as "boring") at $13 TeV$ and that percentage will rise as the C.O.M. energies get higher.

 

[mfb]

That is complicated and above the I level.

 

[Anashim]

That is complicated and above the I level.

It is not my intention to polemicize but, IMO, pomeron(s) exchange is not an explanation unless you relate them to something physical. Please, be aware of the fact that I do not mean to be/look unfriendly and that I am studying Regge's theory myself. But the way I see it, pomeron exchange is a mere tautology: you need a Regge trajectory with $\alpha_P(0)>1$ consistent with Foldy-Peierls theorem to explain the experimental data, so you make up one and call it Pomeron, because of Pomeranchuk theorem.

Now they need to explain why $pp$ and $p\bar p$ cross-sections (total and elastic) are different at high energy so they bring back the old Odderon and introduce it into the model. I know there's no better option but it's difficult for me to see if there's any physics in this or this is just a phenomenological model. If there's any physics in it, it should be able to predict the behaviour at higher energies and/or it should be confronted with other hadron interaction experimental results (which, of course, begs the question of how to asign a coupling constant value to any hadron-pomeron vertex).

 

[Neil Marshall]

I said photons have no shape. Photons and protons are completely different things, despite the similar name. In the quoted part you asked about photons.

Protons are spherical, but they don't have a three-dimensional internal structure. You can't say "this quark is here and that is there".

mfb: I'm sorry if I gave you the impression I was interested in the shape of photons. I could care less. I do care about the shape of a proton when it's accelerated. I agree that the positions and momenta of quarks in a proton cannot be predicted, but we know for sure that they stick together like glue (no pun intended), So I contend that together quarks and gluons occupy space just like the standing wave shells of electrons occupy space. If you told me that gluons mediate that space I would agree. However, the question I'm asking is how do gluons mediate that space. Do gluons (which represent 99% of the mass of a proton) increase in number and/or individual energy levels as acceleration increases? Do quarks begin to separate as the relativistic mass of a proton increases due to acceleration? If so by how much before quark jets begin to propagate? Does acceleration cause a proton which is spherical in shape at rest turn into an ellipsoid at high acceleration? If so, does length contraction play a role? These are questions that may possibly be answered experimentally at the LHC as my colleague and I continue to research the theory.

 

[mfb]

If you told me that gluons mediate that space I would agree.

I don't think that is a meaningful description.

Do gluons (which represent 99% of the mass of a proton)

They don't. The binding energy does, but it is split over gluons and quarks.

Do gluons increase in number and/or individual energy levels as acceleration increases?

There is not even a well-defined "number of gluons in a proton".
The mass doesn't increase (forget relativistic mass. No one uses it and it just leads to confusion), and the internal structure of the proton doesn't change either. You can always look at the proton in its rest frame.
If you get a collision of something from the outside with something in the proton then you have to account for the motion of the proton.

 

[TeethWhitener]

Protons, as everything, get length contracted as seen in the lab frame. As they don't have an actual three-dimensional structure anyway this is nothing you could see.

@mfb This is interesting. The electric quadrupole moment of a nucleus plays a very important role in magnetic resonance experiments. I would think that relativistically flattening out a proton into an oblate spheroid would give it a quadrupole moment that, in principle, would be observable with the right experiment. But I'm not even sure the idea is well-posed.