why does mass increase with increase in speed?

Question

1.actually does this happen only for objects comparable to speed of light or for every object moving with any speed?

2.also why does this happen?

3. also is light mass less? i think it is, then what about this. E=mc^2
if light has 0 mass then E=0 right? what does that mean? light has no energy? then how does it affect our lives?

sorry for asking so many question in one chance, but please do answer me.
thanks..

Answer 1

On 1 and 2: MASS IS NOT VELOCITY DEPENDENT! Despite what you are being told in class, the relativistic mass concept is a misguided way to keep the expression for momentum the same as the classical expression p = m v. In relativity,



p = m v / sqrt(1-v^2/c^2) , and there is NO GOOD reason to attribute the denominator to the mass to keep the form p = m v, but now with m being velocity dependent. m(v) = m(0)/sqrt(1-v^2/c^2).

But why would you want to hold on to an expression that is classical...? This velocity dependent mass stuff came into lectures in the 1950's and some students of then became professors of now but modern treatments have banned this didactical mistake.



Moreover, mass in relativity is an invariant, because it is the length of a four-vector. You cannot have it both ways. So forget about velocity-dependent mass, because its introduction was a didactical mistake!

EDIT the momentum four-vector (E/c, p) has length-squared given by E^2 / c^2 - p^2 ( Minkowskian instead of Euclidean inner product) This equals m^2 c^2. But in the theory, the length of a four-vector is the same for all inertial observers (i.e. Invariant). So mass is an invariant of the theory and therefore it does NOT depend on the relative velocity between the mass and the inertial observer. It is the same number m ( it is invariant) for all inertial observers





3. The complete expression relating energy, mass and momentum in relativity is



E = sqrt(m^2 c^4 + c^2 p^2)



A massive particle can have zero momentum (be at rest) and therefore it has rest energy E = m c^2. Note therefore that Einstein's formula better have a subscript zero on E, to make clear it is rest energy...



So energy has two contributors in trelativity: mass and momentum.



A massless particle such as the photon does have momentum, and therefore has energy E = c p (set m=0 in the general expression).



Note that with de Broglie's p = h/lambda you recover for a massless particle like the photon: E = h c / lambda = h f , the Planck relation ;-)





I think a 1950's student just gave me a thumbs down... :-)



@Robert B : As an idiot to a genious like yourself....a photon has energy, so according to you it has mass? Maybe you should share your credentials with us so that we idiots can learn what it takes to become a genious like you!



@nyphdynm... The E in E = m c^2 is REST ENERGY. Don't make the mistake of putting kinetic energy in there and pretend it is rest energy? The correct relativistic expression for energy is



E = mc^2/sqrt(1-v^2/c^2) . Again, you should resist the temptation to associate the square root with m alone . It reduces to E = mc^2 when v=0 .



EDIT2: Lev Okun has written a nice paper: http://www.itep.ru/theor/persons/lab180/okun/em_3.pdf

Answer 2

Mass does not increase with speed. This misinterpretation of relativity was discarded decades ago but still persists in the popular media. When an object increases speed, it increases its kinetic energy. It's true that this kinetic energy can be converted to mass during a collision, but it resides as kinetic energy until the collision.



1. The relativistic expression for kinetic energy (which gets mis-interpreted as relativistic mass) applies to all object with mass at all speeds. At low speeds, the relativistic expression for kinetic energy still applies but it is so close to the classical expression 1/2 mv^2 that the classical expression can be used. Only at speeds close the speed of light is the relativistic expression much different than the classical expression. But it applies at all speeds.



2. It doesn't.



3. Light is massless. E = mc^2 only applies to particles with mass. For massless particles such as light, the expression is E = pc (or E = hf or E = hbar c k, which are all equivalent). Light has energy. Light is pure energy.



4. "Mass is invariant" means that the mass is the same no matter what frame you measure it in. Black holes are perfect examples. If you flew passed a black hole at high speed, in your frame, the black holes would be traveling passed you at high speed. If speed effected mass, the black hole would have more mass in your frame, and thus stronger gravity and a larger event horizon. This doesn't happen.



5. E = mc^2 is only for particles with mass at rest. The full equation is E = mc^2/sqrt(1-u^2/c^2). Also, the momentum p =mv is classical. The relativistic expression is p = mv/sqrt(1-u^2/c^2). Also, this momentum equation applies only to particles with mass. For particles with no mass, the momentum is p = hbar k.



You seem to be mixing up classical equations with relativistic equations and mass equations with massless equations.

Answer 3

"Why does mass increase with increase in speed?"



It doesn't. Special relativity expressly forbids discuss of mass in its formulation. "Relativistic mass" is an infinite number of different scalar values, depending on which direction you accelerate the mass.



"1.actually does this happen only for objects comparable to speed of light or for every object moving with any speed?"



It doesn't at all. Invariant mass = rest mass = inertial mass = gravitational mass =/= "relativistic mass"



"2.also why does this happen?"



Relativistic momentum changes with speed. It just has two terms that are speed dependent for a massive body, one of those being in gamma... 1 / sqrt( 1 - (v/c)^2)



"3. also is light mass less? i think it is, then what about this. E=mc^2"



We looked for mass, it has none. Having mass would also violate conservation of charge.



If you want to consider the correct formula, that talks about other than mass at rest:

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

... where p is relativistic momentum, a vector, and is non-zero for photons (aka light).



"what do you mean by "mass is invariant"? if so how can you explain the formation of a black hole?"



Black holes still have mass.



"this might be silly but isn't p the momentum which is the product of mass and velocity?"



That is in general not correct either.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html



[EDIT:



"I think a 1950s student..."



I suspect it was the person that asked the question. Initial disbelief. They did not ask the question out of disbelief, but to try and highlight what they thought were problems with relativity.

]



[EDIT: "So does this mean that the rest mass has nothing to do with speed?"



"rest" means "speed = 0 in the frame of rest".



"and also how come mass is relative?"



It is NOT, as already described.



"i know that speed and time can be relative coz of time dilation,length contraction etc,"



Be careful here. If I see you moving at 0.8c, you see me (and the rest of the Universe) moving by you at 0.8c. Also, we both agree on the speed of light, c. We only disagree on the speed of a third frame, and we can calculate what each other will measure.



"but i've never come across mass being relative?"



This concept is NOT taught in any current physics textbook. When they do, the teach you only the one formula, and do not teach you the correct formalism, namely:

http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/mass.html

... this is a tool that has more knobs than it should, and as I said before... consideration of any significant mass was intentionally left out of special relativity... so this formula / notion is both misguided, broken, and wrongheaded.



"does the word "relative" refer to different frames of time or is it like this rocket example?"



No it is just a mistake looking for a place to happen, and right now that is in your head. If I could reach out and slap the b*stard that thought up this idea (even if it were Einstein), and the grief and misunderstanding it has caused over the years, I think they woudl not even slap me back.

]



[EDIT:



"... The very foundation of The Special Theory of Relativity is that: Length, Time, and Mass varies relative to the constant speed of light in a vacuum. ..."



Bold faced lie. Special Relativity discounts mass of any sort, and acceleration (but I repeat myself).

]

Answer 4

Hate to take issue with Dr. Z. and no, I'm not a student from the 50's, but one good philosophical view of allowing relativisitc mass to be considered is the following. Let's say your want to accelerate an neutron to the speed of light and you've devised some mechanism to apply force for the acceleration. Now, relativity tells you that as you accelerate the particle, you need to do an ever increasing amount of work which means you need an ever increasing amount of force. As you approach c, the amount of work you must do to get to c becomes infinite. So now you ask, where did all the energy go that I supplied? On explanation is the your old friend E=mc^2 came into play so the energy you supplied went more and more into increasing the relativisitc mass and less into actually accelerating the particle. This is basically the explanaiton out of Ellis' lectures on flat and curved space-time.