Muons

[Peron]

A stationary Muon decays far quicker than a Muon moving near the speed of light. According to the special theory of relativity time dilates, so the decay rate for the moving muon slows down. Because time slows down.

But according to SR something different happens to particles moving close to the speed of light, they gain mass.

 

So could the extra mass account for the slower decay rate of the moving muon?

[Klaynos]

It is perfectly valid, and in most cases prefered, to formulate SR with lorentz invarient mass, this means that the mass does NOT increase.

[timo]

1) The increase in lifetime is perfectly accounted for by boosting the rest frame to a different frame. I do not think someone yet saw a need to account it to something different. That would, of course, not mean that it's impossible or principally wrong to try to do so.

 

2) If in the rest frame you'd increase the mass of the muon, the lifetime would -in very first approximation ignoring the state of the intermediate W boson- decrease. That's because the volume of possible final states increases and hence the decay becomes more likely.

 

So: Yes, by mindlessly rearranging formulas it trivially could: Obtain the Gamov factor from the mass increase (simply from [math]m_\gamma = \gamma m_0[/math]). The factor equals the ratio in decay times (due to [math]t = \gamma \tau[/math]). But conceptually it seems a step backwards because the effect is not similar to the effect a "real" increase in mass (i.e. increase in proper mass) would have; neither quantitatively, nor even qualitatively. Plus, it would be a very "black-boxed" approach this way - it completely ignores any mechanism for decay.

[Peron]

Well doesn't the energy also increase in the Muon which is moving?

[elas]

A stationary Muon decays far quicker than a Muon moving near the speed of light. According to the special theory of relativity time dilates, so the decay rate for the moving muon slows down. Because time slows down.

But according to SR something different happens to particles moving close to the speed of light, they gain mass.

 

So could the extra mass account for the slower decay rate of the moving muon?

 

You are confusing apparent mass with actual mass. Aircraft designers know that even at non-relativistics speeds, the centre of gravity of an object moves forward along the line of advance as speed increases; therefore the mass distribution within the object is altered but the total mass remains unchanged. The apparent mass (measured by collsion; i.e in the direction of travel) increases with speed; the true mass (inappropiately reffered to as the 'rest' mass) remains the same.

Forward of the centre of gravity particles are compressed at right angle to the plane of advance. To the rear of the centre of gravity particles are compressed (elongated) in the direction of advance.

[Peron]

Ok, now I get it their is no "real" mass increase. It's more of a illusion.

[J.C.MacSwell]

You are confusing apparent mass with actual mass. Aircraft designers know that even at non-relativistics speeds, the centre of gravity of an object moves forward along the line of advance as speed increases; therefore the mass distribution within the object is altered but the total mass remains unchanged. The apparent mass (measured by collsion; i.e in the direction of travel) increases with speed; the true mass (inappropiately reffered to as the 'rest' mass) remains the same.

Forward of the centre of gravity particles are compressed at right angle to the plane of advance. To the rear of the centre of gravity particles are compressed (elongated) in the direction of advance.

 

Is all this from a conjecture of your own? Or can you provide a link?

[Klaynos]

You are confusing apparent mass with actual mass. Aircraft designers know that even at non-relativistics speeds, the centre of gravity of an object moves forward along the line of advance as speed increases; therefore the mass distribution within the object is altered but the total mass remains unchanged. The apparent mass (measured by collsion; i.e in the direction of travel) increases with speed; the true mass (inappropiately reffered to as the 'rest' mass) remains the same.

Forward of the centre of gravity particles are compressed at right angle to the plane of advance. To the rear of the centre of gravity particles are compressed (elongated) in the direction of advance.

 

A reference, or keep your own speculations out of the actual science forums.

[Peron]

It is perfectly valid, and in most cases prefered, to formulate SR with lorentz invarient mass, this means that the mass does NOT increase.

 

Well why doesn't the mass increase? I thought particles traveling close to the speed of light, that have mass, convert the energy that is given to them to mass.

[Klaynos]

Well why doesn't the mass increase? I thought particles traveling close to the speed of light, that have mass, convert the energy that is given to them to mass.

 

That is one way of formulating SR, there is another which is often prefered where the mass remains constant. There is still an infinite energy required to reach the speed of light but there is no relativistic mass, only invariant rest mass.

[elas]

A reference, or keep your own speculations out of the actual science forums.

 

There is still an infinite energy required to reach the speed of light but there is no relativistic mass, only invariant rest mass.

 

To be absolutely honest, I thought that I was being particularly careful not to introduce my own interpretation. After a quick search it comes as a complete surprise to realise that the movement of the Centre of mass within a particle field is indeed speculative. I had assumed that the knowledge that this movement of the Centre of mass is responsible for a change in the observed energy of the invariant rest mass was well known; but, on that score I appear to be wrong. Would someone please advise me as to how SR explains the cause of the increase in energy?

[Klaynos]

To be absolutely honest, I thought that I was being particularly careful not to introduce my own interpretation. After a quick search it comes as a complete surprise to realise that the movement of the Centre of mass within a particle field is indeed speculative. I had assumed that the knowledge that this movement of the Centre of mass is responsible for a change in the observed energy of the invariant rest mass was well known; but, on that score I appear to be wrong. Would someone please advise me as to how SR explains the cause of the increase in energy?

 

It is a result of the fixed speed of light. There is no easy analogous explain what is going on, the universe unfortunately doesn't have to be understandable by us

[swansont]

To be absolutely honest, I thought that I was being particularly careful not to introduce my own interpretation. After a quick search it comes as a complete surprise to realise that the movement of the Centre of mass within a particle field is indeed speculative. I had assumed that the knowledge that this movement of the Centre of mass is responsible for a change in the observed energy of the invariant rest mass was well known; but, on that score I appear to be wrong. Would someone please advise me as to how SR explains the cause of the increase in energy?

 

I think the request was for support that aircraft design uses relativity in any way. There are a lot of models that use an "effective mass" (or similar terminology) because it makes the modeling easier, but that does not really seem to be this issue here.

 

In SR, [math]E^2 = p^2c^2 + m^2c^4[/math] where m is the rest/invariant mass.

 

One might choose to define mass as [math]m = \frac{E}{c^2}[/math], but that's not the same thing, as it is frame dependent — these equations will only give the same answer in the rest frame.

[Peron]

To be absolutely honest, I thought that I was being particularly careful not to introduce my own interpretation. After a quick search it comes as a complete surprise to realise that the movement of the Centre of mass within a particle field is indeed speculative. I had assumed that the knowledge that this movement of the Centre of mass is responsible for a change in the observed energy of the invariant rest mass was well known; but, on that score I appear to be wrong. Would someone please advise me as to how SR explains the cause of the increase in energy?

 

"If you push on an object in the direction of motion, it gains momentum and it gains energy. But if the object is already travelling near the speed of light, it can't move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase, but its speed approaches a constant value—the speed of light. This means that in relativity the momentum of an object cannot be a constant times the velocity, nor is the kinetic energy given by 1⁄2mv2.

 

The relativistic mass is defined as the ratio of the momentum of an object to its velocity, and it depends on the motion of the object. If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass. As the object approaches the speed of light, the relativistic mass becomes infinite, because the momentum becomes infinite."

 

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Conservation_of_mass_and_energy

[swansont]

"If you push on an object in the direction of motion, it gains momentum and it gains energy. But if the object is already travelling near the speed of light, it can't move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase, but its speed approaches a constant value—the speed of light. This means that in relativity the momentum of an object cannot be a constant times the velocity, nor is the kinetic energy given by 1⁄2mv2.

 

The relativistic mass is defined as the ratio of the momentum of an object to its velocity, and it depends on the motion of the object. If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass. As the object approaches the speed of light, the relativistic mass becomes infinite, because the momentum becomes infinite."

 

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Conservation_of_mass_and_energy

 

Is there a question here?

 

You can define mass this way. Or you can use the rest/invariant mass. The equations you construct will be different, based on which definition you use. Which is why you must define which mass you are using; you did not do this in your original post. The default for "mass" is the rest mass, in most physics discussions.

[Peron]

"If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass. As the object approaches the speed of light, the relativistic mass becomes infinite, because the momentum becomes infinite.

(http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Conservation_of_mass_and_energy)"

 

The relativistic mass comes from the energy you put into it. But mass is energy, so when the mass increases the energy also increases in the moving object. There should be no reason why this isn't responsible for the slower decay rate.

[swansont]

"If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass. As the object approaches the speed of light, the relativistic mass becomes infinite, because the momentum becomes infinite.

(http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Conservation_of_mass_and_energy)"

 

The relativistic mass comes from the energy you put into it. But mass is energy, so when the mass increases the energy also increases in the moving object. There should be no reason why this isn't responsible for the slower decay rate.

 

I refer you to the answer previously given by Atheist:

 

So: Yes, by mindlessly rearranging formulas it trivially could: Obtain the Gamov factor from the mass increase (simply from [math]m_\gamma = \gamma m_0[/math]). The factor equals the ratio in decay times (due to [math]t = \gamma \tau[/math]). But conceptually it seems a step backwards because the effect is not similar to the effect a "real" increase in mass (i.e. increase in proper mass) would have; neither quantitatively, nor even qualitatively. Plus, it would be a very "black-boxed" approach this way - it completely ignores any mechanism for decay.

[Peron]

I still don't get it, can someone explain it in laymen's terms?

[Severian]

I still don't get it, can someone explain it in laymen's terms?

 

Firstly, do you agree that your definition of mass is frame dependent? Depending on which frame you measure it in you will get a different answer.

 

So it isn't really a fundamental property of only the object, since it is also dependent on you. That makes it a not very useful quantity.

 

But instead, when someone asks you the mass of the object, you could instead tell them what the mass would be if you measured it in the same frame that the object is moving in. That way, they can work out the 'mass' (in whatever definition they like, without worrying about your frame - you don't need to send them as much information.

 

This quantity is known as the 'rest mass' because it is the mass as measured in the rest frame of the object, but it is now used so exclusively in serious science that people just usually call it the mass.

[Peron]

So your saying that the mass doesnt rise?

[swansont]

So your saying that the mass doesnt rise?

 

Using the definition of mass that is most commonly used, no, it doesn't.

[Peron]

So, what we measure as mass increase is actually relativistic momentum.

 

Here in Einstein's own words,

"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

Edited October 4, 2009 by Peron
Consecutive posts merged.