Transfer speeds of forces affected by time dilation?

[jaketodd]

Are forces subject to the Lorentz transformation? Not force carriers; I already got that question answered, thanks to @PeterDonis. But forces. The different forms of them, such as the contact forces etc.: https://en.wikipedia.org/wiki/Contact_force

With time dilation, does the rate of force transfer, from one thing to another, slow down as well as the clocks, to an external observer?

As the speed of a system approaches the speed of light, do the forces within that system, approach zero speed/occurrence?

I don't think I can find a paper or textbook on this. I searched arxiv and google scholar, but did not find anything.

Thanks,

Jake

 

[PeterDonis]

Are forces subject to the Lorentz transformation?

Yes. Like any other quantity in a relativistic theory, you must represent forces by geometric objects that transform correctly under a change of frames. In the case of forces, this will mean 4-vectors.

With time dilation, does the rate of force transfer, from one thing to another, slow down as well as the clocks, to an external observer?

What does "rate of force transfer" even mean?

You might want to find a specific example of a scenario that illustrates what you are asking about.

 

[Ibix]

The different forms of them, such as the contact forces etc.: https://en.wikipedia.org/wiki/Contact_force

They're pretty much all the electromagnetic force between the electrons of one object and another.

With time dilation, does the rate of force transfer, from one thing to another, slow down as well as the clocks, to an external observer?

"Rate of force transfer" doesn't make sense, I'm afraid. Forces don't transfer, so I don't think your question has an answer.

I'm not really sure what you are trying to ask. I would say something like "all processes are affected by time dilation", which is broadly true, but it's frequently more than that. For example, an interaction that one frame interprets as purely electrostatic another frame will interpret as both electric and magnetic.

 

[Dale]

Are forces subject to the Lorentz transformation?

Yes.

In relativity quantities that seem separate get grouped together. Like time gets grouped together with space to form spacetime.

Similarly, energy gets grouped together with momentum to form the four-momentum. In the four-momentum energy has the same relationship to momentum as time has to space. So energy and momentum Lorentz transform together just like time and space do.

Force is the rate of transfer of momentum, and power is the rate of transfer of energy. So it should come as no surprise that power and force get grouped together in the four-force. Power and force thus Lorentz transform together just like time and space.

For details see https://en.m.wikipedia.org/wiki/Four-force

 

[malawi_glenn]

I am trying to make sense what "force transfer" is referring to. Do you mean something like this, there are a bunch of balls lying next to eachother. Another ball is incomming from the left. How long time after the left ball has made contact, will the ball farthest to the right start to move? Sort of a Newtonian cradle thing?

 

[jbriggs444]

A "force" is already a rate of momentum transfer. So the proper question to ask would be whether the Lorentz transform affects the rate of momentum transfer from one system to another. As @PeterDonis pointed out in #2, forces (aka rates of momentum transfer) are affected by the Lorentz transform.

 

[PeterDonis]

the rate of force transfer

@jaketodd you now have several posters in this thread who are confused about what this means. You need to clarify. As I said in post #2, a specific scenario would help.

 

[jaketodd]

@jaketodd you now have several posters in this thread who are confused about what this means. You need to clarify. As I said in post #2, a specific scenario would help.

I like this one:

I am trying to make sense what "force transfer" is referring to. Do you mean something like this, there are a bunch of balls lying next to eachother. Another ball is incomming from the left. How long time after the left ball has made contact, will the ball farthest to the right start to move? Sort of a Newtonian cradle thing?
View attachment 328392
View attachment 328393

But there are many other forces, other than contact forces/contact interactions:
https://www.google.com/search?q=list+of+forces+in+physics

 

[PeterDonis]

I like this one

That one drags in a lot of issues that are quite possibly too complex for this level of discussion. For example, the rate at which the effects of an applied force at one end of a solid object travel through the object to the other end depends on the object's material properties; in the simplest approximation it can be taken to be the speed of sound in the object, but there are many possible corrections. But the speed of sound in the object has nothing to do with relativity or Lorentz transformations.

there are many other forces

Yes, and that makes the field of discussion much too wide for a PF thread. The basic question you asked in your OP has already been answered. If you want to focus on one single scenario to see how that answer plays out, that would be fine, but then the thread needs to stay focused on just that one scenario.

 

[jaketodd]

If you want to focus on one single scenario to see how that answer plays out, that would be fine, but then the thread needs to stay focused on just that one scenario.

One at a time...

How about nuclear fusion inside the sun?
If the sun were moving at relativistic speed, relative to you, would the sun be less bright?

Thanks,

Jake

 

[Ibix]

How about nuclear fusion inside the sun?
If the sun were moving at relativistic speed, relative to you, would the sun be less bright?

Depends what you mean. The emission is no longer isotropic, so for an individual observer the Sun might be very, very bright (if it's coming more or less directly at you) or almost invisible.

Integrating over the whole Sun though, it should be easy enough to work out. Work in the Sun's rest frame. In some time interval $\delta t$ it loses mass $\delta m$ as radiation so the total energy emitted is $c^2\delta m$ and the power is $c^2\delta m/\delta t$. Now work in the rest frame of the observer. The total energy of the Sun is higher in this frame due to its kinetic energy - so the total energy lost is $\gamma c^2\delta m$. However it takes longer to emit the energy - the time taken is $\gamma\delta t$. So the gammas cancel out of the energy emitted per unit time and the total energy flux does not change.

 

[PeterDonis]

One at a time...

Now you've come up with a totally different scenario that has nothing to do with your original question. Is this thread going to turn into an indeterminate number of questions about "how does relativity affect scenario X?"

Again, your original question was about "force transfer". Your latest question has nothing whatever to do with "force transfer". Do you have a "force transfer" scenario you want to discuss, or has that question been sufficiently answered?

A different question having nothing to do with "force transfer" belongs in a new thread.

 

[Dale]

@jaketodd In post 4, I gave a pretty complete answer regarding forces in relativity. Before moving to nuclear reactions, do you have any follow-up questions on that?

It is a little disheartening to answer a question with a careful, informative, complete, and non-technical response to just have the targets changed suddenly.

 

[jaketodd]

Ok next up, electricity: If a light bulb is moving at relativistic speed, would it seem less bright, since the electrons, which power it, are moving more slowly to an external observer?

And yes, @PeterDonis this is a force transfer, when the electrons heat the light bulb filament and give off photons.

And yes, @Dale, electrons are not always possessing momemtum, other than spin.

@Ibix Sounds like the doppler effect of light.

Thanks All,

Jake

 

[jbriggs444]

Ok next up, electricity: If a light bulb is moving at relativistic speed, would it seem less bright, since the electrons, which power it, are moving more slowly to an external observer?

The rate at which light is given off in the rest frame of the light bulb is easily known. You read it from the label.

The rate at which light is seen by a moving observer can be calculated from this in a straightforward manner without giving any consideration to electrons, filaments, phosphors or whatever. This is a pretty straightforward technique for analysis, even in plain old Newtonian mechanics. You pick a convenient frame where a calculation is straightforward. Then you translate the result to a chosen frame where the quantity is needed.

None of this has anything to do with "force transfer" which is still a meaningless concept.

 

[PeterDonis]

this is a force transfer

No, it's not.

when the electrons heat the light bulb filament and give off photons.

That's an energy and momentum transfer, not a force transfer.

 

[PeterDonis]

Thread closed for moderation.

 

[Nugatory]

Ok next up, electricity:

What part of "A different question having nothing to do with 'force transfer' belongs in a new thread" did you not understand?

 

[PeterDonis]

After moderator review, this thread will remain closed as the OP question has been answered. Thanks to all who participated.