What is relativistic mass?

Not being matter, it possesses no mass. If it did, it couldn't move at the speed of light. It does have momentum, though, and so, an effective mass in that sense.

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I've read very little on this subject, so excuse my ignorance...

One of the first applications of limits I learned in Calculus was that as you approach the speed of light, your mass approaches zero. So, does this imply that if you slow photons down, they have mass?

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As any matter approaches the speed of light, its mass becomes infinite, not zero. You cannot slow photons down except by having them propagate through matter, which does reduce their speed, at least in a sense, but still does not give them mass. Photons do not possess mass - period.

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Brandon, please let me know how accurate the following is:

Quote:

Here's a way to recognize the relationship of mass to the speed of light:

F=MA (Force = Mass times Acceleration)

If your reduce Mass to zero, then Force also goes to zero, so if you had a particle with zero mass, then zero force would be required to accelerate it to in infinite velocity.

As a result, no massless particle can exist at any velocity other than an infiinte one

Is that stated correctly, or should I use "speed" instead of "velocity"?

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Velocity requires direction right? So maybe it's better to use speed.

Quote:

Not being matter, it possesses no mass. If it did, it couldn't move at the speed of light. It does have momentum, though, and so, an effective mass in that sense.

p=mv?

Yeah I've done an experiment where a beam of focused light can move a leaf in water, I guess this shows its momentum, but I still don't get how it can have momentum and be said to have no mass.

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Ray wrote:

Velocity requires direction right? So maybe it's better to use speed.

Yeh, I was wondering the same thing.

Ray wrote:

Quote:
Not being matter, it possesses no mass. If it did, it couldn't move at the speed of light. It does have momentum, though, and so, an effective mass in that sense.

p=mv?

Yeah I've done an experiment where a beam of focused light can move a leaf in water, I guess this shows its momentum, but I still don't get how it can have momentum and be said to have no mass.

I'm not sure either (at least from a math perspective).

I've seen the explanations for relativistic mass before, but am not sure how to relate it to momentum mathematically.

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Quote:

If your reduce Mass to zero, then Force also goes to zero, so if you had a particle with zero mass, then zero force would be required to accelerate it to in infinite velocity.

No...if you have zero force, then you have the tautology 0=0 which doesn't tell you anything

Quote:

As a result, no massless particle can exist at any velocity other than an infiinte one

there is no such thing as infinite velocity, light does not travel at infinite velocity it travels at 3x10^8 m/s in a vaccuum like all other EM waves

Einstein's equation of relativity states:

E2 = m2c4 + p2c2

Here you see that mass depends on p which is momentum which usually depends on velocity....this is relativistic mass, your general all around "mass"

however, If for some reason, you wanted to IGNORE the velocity of the particle, then p=0...and then the equation simplifies to:

E = mc^2

this looks familiar doesn't it? here, mass is not the same because it ignores the velocity of the particle....so this is called "rest mass" or "invariant mass"...whatever, nobody seems to use it anymore

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There is no such a thing as "relativistic mass", and as stuh505 put in the reply above, the formula

E^2 = (mc^2)^2+(pc)^2

tells most things.

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the term "relativistic mass" is one that is helpful to distinguish from rest mass...it is commonly used...usually when people say "mass" they mean the same thing as "relativistic mass"

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Some authors (F. Taylor & John Archibald Wheeler) adovocate to avoid the idea and the term of "relativistic mass." But it may of use to know that some other autors use the term.

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satt,

I'll wager that their advocation stems from a simultaneous admonishment of the term and concept of rest mass...but when the topic of conversation turns to rest mass, I don't see how we can avoid referring to the mass that is relativistic as being relativistic, simply as a means of distinguishing it in communication!

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We can use the concept of "momentum" throughout..

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Light is both a particle (albeit mass-less) and a wave and exhibits both characteristics. A wave could not travel through a vacuum, but a particle would not produce distinct refractive patterns - light does both.

What light does have is 'momentum' which can be imparted to objects (ie a space-sail). If you are heading down the path of 'light is deflected by gravity masses' the answer is that what is happening is 'lensing'. The light is travelling a straight line along space that has been warped by a massive object such as a black hole.

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rosborne979 wrote:

Brandon, please let me know how accurate the following is:

Quote:
Here's a way to recognize the relationship of mass to the speed of light:

F=MA (Force = Mass times Acceleration)

If your reduce Mass to zero, then Force also goes to zero, so if you had a particle with zero mass, then zero force would be required to accelerate it to in infinite velocity.

As a result, no massless particle can exist at any velocity other than an infiinte one

Is that stated correctly, or should I use "speed" instead of "velocity"?

F=MA is only a correct formula at speeds low compared to light, but F = dP/dt is correct at any speed (P = momentum, and t = time), where P is being differentiated with respect to time. The momentum, P, involves both the body's mass and its velocity. I am not sure if it applies to light, which is usually treated by quantum electrodynamics. It is true that all objects with zero mass travel at the speed of light. Velocity and speed differ only in that the former is a vector quantity including direction.

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Ray wrote:

...I've done an experiment where a beam of focused light can move a leaf in water, I guess this shows its momentum, but I still don't get how it can have momentum and be said to have no mass.

I suspect that your experiment involves only heating of the leaf and/or water, since the momentum of any beam available to us would probably be too low to produce this effect. The same is true of the "radiometer effect."

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I meant 'diffractive patterns' no refractive. My bad.

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What is relativistic mass?

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