Muons magnetic field time dilation

In summary: Graviton coupling is universal, which implies a kind of absolute sensitivity to energy-momentum, and in particular that the gravitational time dilation is a manifestation of this sensitivity.This post from the dawn of time elaborates on this a bit more.This post from the dawn of time elaborates on this a bit more.
  • #1
kodama
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muons mean lifetime of 2.2 µs

muons in a strong gravitational field or traveling at relativistic speeds experience time dilation

would a muon in a strong magnetic field, say near a magnetar experience additional time dilation more than a muon in an non-magnetic field with the same gravitational strength, accounting for the stress-energy tensor of the magnetic field?
 
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  • #2
A strong magnetic field has a high energy density which contributes to the gravitational potential. Yes, but the effect is tiny.
 
  • #3
mfb said:
A strong magnetic field has a high energy density which contributes to the gravitational potential. Yes, but the effect is tiny.

but is it greater than a muon in gravitational potential of equal strength, but no magnetic field
 
  • #4
It does not depend on the field strength, it depends on the potential, which depends on the overall field geometry, and the energy density of electromagnetic fields is small. As an example, the atmosphere of Earth has a density of 1.3 kg/m3 or 1.2*1018 J/m3. To get the same energy density with a magnetic field, you need 1.2 MT (Megatesla). To match the density of water, you need 34 MT.

With 10 GT, you get a density of 4.4*108 kg/m3. That sounds large, but it is smaller than even the neutron star crust density of ~109 kg/m3, and tiny compared to the average density of a few 1017 kg/m3.
 
  • #5
I understand that.

the reason i am asking is that gravitons are bosons of spin-2, photons gluons w z are bosons of spin-1

dealing only with a QFT description of gravity as gravitons, not curved spacetime as in GR,

is there a deep reason that gravitons bosons by themselves can cause time dilation but other types of bosons like photons gluons w-z by themselves don't cause time dilaton, only via their effects via energy density?
 
  • #6
There is no fundamental difference between photons, gluons, W, Z and all the fermions in that aspect. They all just contribute via their energy.
I don't think "gravitons cause time dilation" is a meaningful description, because it is not the local field strength that matters.
 
  • #7
mfb said:
There is no fundamental difference between photons, gluons, W, Z and all the fermions in that aspect. They all just contribute via their energy.
I don't think "gravitons cause time dilation" is a meaningful description, because it is not the local field strength that matters.

here we are describing gravity solely in terms of gravitons on flat QFT, not curved spacetime as in GR.

the interactions of a photon with a charged fermion by itself doesn't cause any time dilation, but interactions between gravitons with fermions via energy does cause time dilation.

so what special properties does a massless spin-2 boson cause time dilation that a massless spin-1 boson does not?
 
  • #8
kodama said:
here we are describing gravity solely in terms of gravitons on flat QFT, not curved spacetime as in GR.

the interactions of a photon with a charged fermion by itself doesn't cause any time dilation, but interactions between gravitons with fermions via energy does cause time dilation.
Can you please provide a reference dealing with what you are actually asking (the model in which framework we are talking)?
 
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  • #10
mitchell porter said:
See this post from the dawn of time.

doesn't it violate the equivalence principle that 1 ev energy worth of massless spin-1 bosons photons and gluons doesn't dilate time as much as 1ev worth of massless spin-2 gravitons for a test particle?
 
  • #11
kodama said:
that 1 ev energy worth of massless spin-1 bosons photons and gluons doesn't dilate time as much as 1ev worth of massless spin-2 gravitons for a test particle
Who claims that?

You are mixing real and virtual particles here I think.
 
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  • #12
The core question is
kodama said:
what special properties does a massless spin-2 boson cause time dilation that a massless spin-1 boson does not?

If I consult the Feynman Lectures on Gravitation, as suggested in the link I posted, I find Feynman contrasting particle motion in an electromagnetic field and in a gravitational field, as follows: "the gravitational equation has a qualitatively distinct new feature; not only the gradients, but also the potentials themselves appear in the equations of motion" (5.2.1).

From this he derives the gravitational time dilation. It seems to be a "timelike" manifestation of the fact that gravity is sensitive, not just to potential energy differences ("the gradients"), but to the absolute amount of energy ("the potentials themselves").

Meanwhile, I believe this universality of gravity can be deduced quantum mechanically, by considering the amplitude for emitting a massless spin-2 particle in the limit where the particle has zero momentum, we show that the coupling to all forms of energy-momentum is the same (I am referring to "Weinberg's low-energy theorem"). The analogous argument for a massless spin-1 boson only implies charge conservation.

So, my schema for explaining this is, low-energy theorem implies graviton coupling is universal, which implies a kind of absolute sensitivity to energy-momentum, and in particular that the speed of a physical process depends on the gravitational potential.

I am not 100% sure that I have it right, even schematically; and there is probably also a more geometric account of this, based on spin-2 mapping to a metric, but spin-1 only to a connection. But the combination of Weinberg and Feynman, correctly interpreted, surely has the kernel of an answer.
 
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  • #13
mitchell porter said:
If I consult the Feynman Lectures on Gravitation, as suggested in the link I posted, I find Feynman contrasting particle motion in an electromagnetic field and in a gravitational field, as follows: "the gravitational equation has a qualitatively distinct new feature; not only the gradients, but also the potentials themselves appear in the equations of motion" (5.2.1).
I think that as a statement is kind of simplified... for example a scalar charged particle that interacts electromagnetically, will also have the EM potential in its equation of motion (which is given by replacing the partial derivatives by the covariant derivatives including the electromagnetic field). The introduction of covariant derivatives looks pretty similar to how they are introduced in general relativity, but for different topologies (eg in GR you have them introduced for covariance along translations of vectors over the spacetime manifold, while in the Electromagnetism case it does almost the same for covariance along redefinitions of the EM field allowed by the U(1) local symmetry). The EM field in this case looks very similar to the Christoffel symbols (the Connections).
[itex] D_\mu D^\mu \phi = ( \partial_\mu + ig A_\mu )^2 \phi = m^2 \phi \Rightarrow \partial^2 \phi - ig \phi \partial_\mu A^\mu+ A^2 \phi + (\partial_\mu K^\mu)= m^2 \phi [/itex]
 

What is a muon?

A muon is a subatomic particle that is similar to an electron but with a much greater mass. It is classified as a lepton and is typically created when cosmic rays collide with particles in the Earth's atmosphere.

What is the magnetic field of a muon?

The magnetic field of a muon is the force created by the muon's movement through space. This magnetic field is created by the muon's charge and its mass.

What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for an object that is moving at high speeds. This is a fundamental principle of Einstein's theory of relativity and is caused by the warping of space-time.

How does the magnetic field affect time dilation in muons?

The magnetic field of a muon can affect its time dilation by altering its trajectory and speed. This means that muons with higher magnetic fields will experience greater time dilation compared to muons with lower magnetic fields.

Why is studying muons and their magnetic field important?

Studying muons and their magnetic field is important because it can help us better understand the fundamental laws of physics, such as relativity. It also has practical applications in fields like particle physics and astrophysics, where the behavior of subatomic particles is crucial to understanding the universe.

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