Can energy be stored in a single particle indefinitely?

[Suekdccia]

TL;DR Summary

Can energy be stored in a single particle without it being lost over time?

Can energy be stored in a single particle without it being lost over time?


I mean, photons would be an exampld in principle, but they get redshifted as the universe expands and become less energetic as time goes by


We could store that energy in form of kinetic energy for individual particles, but similarly, they would lose that energy as particles tend to be at rest, losing kinetic energy as spacetime expands


Angular momentun does not redhsift in principle, but the angular momentum of individual particles is a quantum one and cannot be transferred, so that "energy" would never be accessible (it would be as if the particle contained no energy at all)


Therefore, is there any way in which an individual particle would store energy but in a way that would not be "redshifted" or degraded consistently over time?

 

[Nugatory]

The energy of a closed system comprised of a single particle does not change over time.

 

[Suekdccia]

The energy of a closed system comprised of a single particle does not change over time.

But what about cosmic rays travelling through the universe? The expansion of spacetime does "redshift" their speed in a similar way to how it redshifts light frequency. Therefore, particles such as these will tend to be at resr in the future, losing their kinetic energy over time. That's what I was referring to

Therefore, is there any way in which energy could be stored in a single particle (or two at most) and would not be lost despite the expansion of the universe?

 

[PeroK]

But what about cosmic rays travelling through the universe? The expansion of spacetime does "redshift" their speed in a similar way to how it redshifts light frequency. Therefore, particles such as these will tend to be at resr in the future, losing their kinetic energy over time. That's what I was referring to

Speed and kinetic energy depend on your frame of reference. No particle can be said to be absolutely at rest.

 

[Nugatory]

Therefore, is there any way in which energy could be stored in a single particle (or two at most) and would not be lost despite the expansion of the universe?

Draw an imaginary and arbitrarily small box around the particle. As long as no energy crosses the sides of the box, the amount of energy inside the box does not change.

 

[PeterDonis]

is there any way in which energy could be stored in a single particle (or two at most) and would not be lost despite the expansion of the universe?

You need to rephrase your question, because the loss of kinetic energy you describe, for example in cosmic rays, as the universe expands is not a "loss of energy". No stress-energy is destroyed; stress-energy is locally conserved.

If your question is, is there any way to avoid the effect you describe as kinetic energy loss, for example in cosmic rays, as the universe expands, the answer is no. It happens to everything. (Well, except dark energy, but dark energy is not made of "particles" and there is no way to "store" energy in dark energy--it's constant and we can't change it.)

 

[Suekdccia]

You need to rephrase your question, because the loss of kinetic energy you describe, for example in cosmic rays, as the universe expands is not a "loss of energy". No stress-energy is destroyed; stress-energy is locally conserved.

If your question is, is there any way to avoid the effect you describe as kinetic energy loss, for example in cosmic rays, as the universe expands, the answer is no. It happens to everything. (Well, except dark energy, but dark energy is not made of "particles" and there is no way to "store" energy in dark energy--it's constant and we can't change it.)

Mmmh let me see if I understand it correctly

Change a particle for a planet and an alien living on it. The planet has a given velocity and there is no friction (so it does not lose energy from gas clouds or tidal interactions with other massive bodies). After an enormous amount of time, the alien uses a telescope and several other instruments to measure the speed of its planet. Will he measure a decrease on the speed? If the energy is conserved locally, shouldn't they measure the same speed as "x" years before?

In case the alien would measure that the speed has decreased then, and returning to the example with cosmic rays and particles, couldn't we use other properties like angular momentum (spin) to store a given amount of energy (as angular momentum or spin of single bodied does not change, even in an expanding universe)? I mean, angular momentum for single particles cannot be extracted (as the angular momentum is a quanrum property) but, are there any other ways? Perhaps using a pair of particles bounded to each other and give them a certain amount of angular momentum?

 

[PeterDonis]

the alien uses a telescope and several other instruments to measure the speed of its planet

There is no such thing as "the speed" of anything. What is the speed being measured relative to?

 

[Suekdccia]

There is no such thing as "the speed" of anything. What is the speed being measured relative to?

Just as we measure the Earth's travelling speed, or our galaxy speed, comparing the planet's speed through the cosmic background radiation or looking for other galaxies and clusters as reference...

 

[Vanadium 50]

There is nothing more special about the frame where the CMBR is at relative rest than the frame where the origin is where and when Abraham Lincoln was shot.

(Less, actually, but one misconception at a time)

 

[PeterDonis]

Just as we measure the Earth's travelling speed, or our galaxy speed, comparing the planet's speed through the cosmic background radiation or looking for other galaxies and clusters as reference...

Ok, so you are defining "speed" relative to the CMBR "rest frame" (the frame in which the CMBR looks isotropic)?

 

[Suekdccia]

Ok, so you are defining "speed" relative to the CMBR "rest frame" (the frame in which the CMBR looks isotropic)?

Yes, the alien's planet motion causes anisotropy through simple Doppler shifting: the CMB photons coming from the direction we're currently heading towards get blueshifted, the photons in the opposite direction get redshifted.

In that way shouldn't the alien be able to measure if the planet suffers any changes in its speed and whether it actually loses kinetic energy due to the expansion of spacetime? How would he measure a decrease in the planet's speed/kinetic energy?

 

[Drakkith]

In that way shouldn't the alien be able to measure if the planet suffers any changes in its speed and whether it actually loses kinetic energy due to the expansion of spacetime?

They can measure a change in speed relative to the CMB, sure, but such a loss in speed would not be because of the expansion of the universe. All expansion does is change the wavelength/frequency of the radiation by some factor, and this change is the same in all directions. In other words, if the CMB is redshifted to half its frequency in one direction, the radiation opposite of it would also be redshifted to half it's previous frequency, even if those frequencies are slightly different because the planet has some nonzero velocity relative to the CMB rest frame.

Note that this is measuring the planet's velocity relative to the CMB's rest frame. Measuring the velocity relative to some other frame my result in a change in velocity over time. For example, two objects moving away from each other will tend to observe an increase in their recession velocities over time as long as they are unbound from each other and far from large masses that would otherwise prevent the metric expansion of space from occurring, while two objects moving towards each other in this situation would gradually see a decrease in their approach velocities.

Also remember that energy is a property of systems of objects, not single particles. Saying, "the electron has 5 MeV of energy" is meaningless without context.

 

[PeterDonis]

shouldn't the alien be able to measure if the planet suffers any changes in its speed

They can measure a change in speed relative to the CMB, yes.

whether it actually loses kinetic energy due to the expansion of spacetime?

That's not a measurement, that's an interpretation. They can interpret their measurement of a change in speed relative to the CMB as a change in their kinetic energy relative to comoving observers, or, if you like, relative to the average distribution of matter in the universe. Our best current model does indeed predict that they would measure such a change, if their planet is not part of any other gravitationally bound system like a galaxy or galaxy cluster.

So, for example, we on Earth would not measure any such change due to expansion, because our solar system is part of a galaxy, which in turn is part of a galaxy cluster. We would measure a change in the direction of our motion relative to the CMB over time (though it would take millions of years for the change to be large enough to be detectable) due to our orbit around the center of the Milky Way and the Milky Way's orbit within the galaxy cluster. But that's not the same thing as the effect of expansion described above.

However, this change in kinetic energy is not a violation of any conservation law, nor does the change have to be compensated by a corresponding change anywhere else. And, as I have already said, there is no way to avoid the change. It's an unavoidable effect of expansion.

 

[PeterDonis]

They can measure a change in speed relative to the CMB, sure, but such a loss in speed would not be because of the expansion of the universe.

Yes, it would.

All expansion does is change the wavelength/frequency of the radiation by some factor

No, that's not all it does. See my post #14 just now.

If you want a general heuristic, any object that has momentum relative to comoving observers will gradually lose that relative momentum as the universe expands, because the average of all the stress-energy in the universe "pulls" on the object and makes its motion approach comoving motion. For radiation, the momentum loss appears as redshift. For matter, the momentum loss appears as a loss of speed relative to comoving observers.

Also remember that energy is a property of systems of objects

The system here is all the stress-energy in the universe, and the motion of an object relative to that.

 

[Drakkith]

If you want a general heuristic, any object that has momentum relative to comoving observers will gradually lose that relative momentum as the universe expands, because the average of all the stress-energy in the universe "pulls" on the object and makes its motion approach comoving motion. For radiation, the momentum loss appears as redshift. For matter, the momentum loss appears as a loss of speed relative to comoving observers.

I see. My mistake then.

 

[Suekdccia]

They can measure a change in speed relative to the CMB, yes.


That's not a measurement, that's an interpretation. They can interpret their measurement of a change in speed relative to the CMB as a change in their kinetic energy relative to comoving observers, or, if you like, relative to the average distribution of matter in the universe. Our best current model does indeed predict that they would measure such a change, if their planet is not part of any other gravitationally bound system like a galaxy or galaxy cluster.

So, for example, we on Earth would not measure any such change due to expansion, because our solar system is part of a galaxy, which in turn is part of a galaxy cluster. We would measure a change in the direction of our motion relative to the CMB over time (though it would take millions of years for the change to be large enough to be detectable) due to our orbit around the center of the Milky Way and the Milky Way's orbit within the galaxy cluster. But that's not the same thing as the effect of expansion described above.

However, this change in kinetic energy is not a violation of any conservation law, nor does the change have to be compensated by a corresponding change anywhere else. And, as I have already said, there is no way to avoid the change. It's an unavoidable effect of expansion.

I see...

Then, if we can interpet this as objects losing velocity relative to comoving objects, then what would happen in this case:

If the vacuum of the universe is metastable it could be transformed into a true one via a cosmic ray (their energy could be enough to surpass the potential to cause a vacuum decay).

But if cosmic rays are losing velocity relative to other comoving objects, would they still be able to "inject" energy into the false vacuum to transform it into a true one?

 

[PeterDonis]

If cosmic rays are losing velocity relative to other comoving objects, would they still be able to "inject" energy into the false vacuum to transform it into a true one?

I don't think triggering a transition from false vacuum to true vacuum works this way. So I don't think your scenario here is well posed and I don't know how to answer your question.

 

[Mordred]

I don't think triggering a transition from false vacuum to true vacuum works this way. So I don't think your scenario here is well posed and I don't know how to answer your question.

I agree the question is poorly described. I do understand the metastability with regards to the inflaton and Higgs field and I cannot answer the question as stated.

 

[Suekdccia]

I don't think triggering a transition from false vacuum to true vacuum works this way. So I don't think your scenario here is well posed and I don't know how to answer your question.

I agree the question is poorly described. I do understand the metastability with regards to the inflaton and Higgs field and I cannot answer the question as stated.

Perhaps I worded it unclearly, here's a reference

https://arxiv.org/abs/hep-ph/9704431

 

[Mordred]

Yes very poorly worded. The answer in this is no.
The process of that paper requires energy levels that only potentially exist prior to electroweak symmetry breaking and this paper further requires that the process occurs prior the the Higgs field dropping out of thermal equilibrium.
It is an examination of a process describing in essence an inflationary process (However most inflationary models use spontaneous symmetry breaking) this paper shows it favors that process rather than a cosmic ray induced process. (Specified in its conclusion).

I should note that this paper is an alternative method prior to discovery of the Higgs boson when the VeV of the Higgs field is not well known via the Higgs mass term.
We now know the Higgs mass and subsequently the VeV (vacuum expectation value) so the process in the paper in essence becomes in essence highly unlikely to have ever occurred.

 

[Suekdccia]

Yes very poorly worded. The answer in this is no.
The process of that paper requires energy levels that only potentially exist prior to electroweak symmetry breaking and this paper further requires that the process occurs prior the the Higgs field dropping out of thermal equilibrium.
It is an examination of a process describing in essence an inflationary process (However most inflationary models use spontaneous symmetry breaking) this paper shows it favors that process rather than a cosmic ray induced process. (Specified in its conclusion).

I should note that this paper is an alternative method prior to discovery of the Higgs boson when the VeV of the Higgs field is not well known via the Higgs mass term.
We now know the Higgs mass and subsequently the VeV (vacuum expectation value) so the process in the paper in essence becomes in essence highly unlikely to have ever occurred.

Then let's consider an easier example:

Let's imagine two particles travelling through the universe and eventually they meet and collapse. If they would have enough energy they could create a black hole in principle. However, if the cosmic expansion does make the particles lose velocity relative to comoving objects, couldn't this avoid that they collide with enough speed to make a black hole?

 

[weirdoguy]

eventually they meet and collapse

And what would that even mean?

If they would have enough energy they could create a black hole in principle.

No they could not.

couldn't this avoid that they collide with enough speed to make a black hole?

You've been told multiple times that speed is relative.

What is the point of this thread?

 

[PeterDonis]

If they would have enough energy they could create a black hole in principle.

Energy in what frame?

 

[PeterDonis]

No they could not.

Actually, two colliding objects could form a black hole under the right conditions. But one has to be careful to specify the right conditions.

 

[Suekdccia]

You've been told multiple times that speed is relative.

What is the point of this thread?

the thing is that I'm having a bit of trouble picturing this. If I still not understand it what should I do? Shut up and stop asking?

Again, as I said in post #22, if the cosmic expansion does make the particles lose velocity relative to comoving objects, couldn't this avoid that they collide with enough speed to make a black hole?

No they could not

As PeterDonis said, it depends on the conditions, but is possible that two colliding objects could from a black hole. Why would you categorically say that is impossible if that's not really true?

 

[Suekdccia]

Energy in what frame?

Kinetic energy from their relative speed to comoving objects.

I mean, if two really energetic particles (like cosmic rays but we can consider any other object like for instance neutron stars as well), and by energetic I mean travelling at enormous speed, and they collide now, they could form a black hole if the right conditions are met.

However, if the same very objects eventually collide far away into the future (and we ignore any possible losses of speed due to gravitational interactions with other objects, friction...) the expansion of the universe would make them lose speed relative to comoving objects. Would this mean that if they meet in the future, since they have lost speed relative to comoving objects, then the collision would be weaker and no black hole could form?

What I'm having trouble with is that, on the one hand stress-eneegy is locally conserved but on the other hand expansion makes the objects lose kinetic energy relative to comoving objects and "forces" it to approach comoving motion. So at the end, I don't really know what would happen in the collision of such particles. Would it be weaker than if two particles collide in a short period of time (where expansion has not decreased their momentum yet)? Would it have the same strength?

 

[PeterDonis]

Kinetic energy from their relative speed to comoving objects.

That is only relevant if they are colliding with comoving objects.

If they are colliding with each other, the relevant energy is the total energy in their center of mass frame.

What I'm having trouble with is that, on the one hand stress-eneegy is locally conserved but on the other hand expansion makes the objects lose kinetic energy relative to comoving objects and "forces" it to approach comoving motion.

This assumes that the objects are test objects--meaning their own energy is negligible. But of course if that's the case they won't form black holes if they collide--because their own energy is negligible.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

After moderator review, the thread will remain closed. The OP question has been sufficiently addressed.