Einstein's Theory of Special relativity

[Science Proff]

I was wondering if anyone could tell me whether a body travelling at a velocity close to the speed of light would have the same mass as its rest mass since Einstein's theory of special relativity says that:

M0=M1/Underroot1-(Beta)2

Where M0=Rest Mass
and M1=Mass at that speed

[ZapperZ]

You are asking about the "relativistic mass", which of course, when presented in that equation, is velocity dependent.

However, please note that the concept of "relativistic mass" is a bit outdated and, rightly so, being considered to be rather inaccurate[1,2]. What is more accurate is the concept of relativistic MOMENTUM. Even Einstein reportedly stopped using the phrase "relativistic mass" shortly after his relativity papers[3].

So you may want to reconsider if you really want to perpetuate such misunderstanding.

Zz.

[1] L.B. Okun Am. J. Phys. v.77, p.430 (2009).
[2] http://arxiv.org/abs/1010.5400
[3] E. Hecht, Am. J. Phys. v.77, p.799 (2009).

[harrylin]

I was wondering if anyone could tell me whether a body travelling at a velocity close to the speed of light would have the same mass as its rest mass since Einstein's theory of special relativity says that:

M0=M1/Underroot1-(Beta)2

Where M0=Rest Mass
and M1=Mass at that speed

Due to different definitions of mass, there can be some confusion. However, as long as you specify it there is nothing ambiguous about it: The rest mass does not change (it's measured in rest!) while the dynamic or relativistic mass is a function of speed, just like length and clock frequency (compare "rest length" and "proper time").

Note that the definition that Einstein used in 1905 was again different. A neutral discussion of "relativistic mass" can be found in the physics FAQ (with which I helped a little):

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Harald

[Science Proff]

Well let me get this straight. Is the theory of special relativity true?
I mean can mass be changed just by changing its speed close to the speed of light?

[harrylin]

Well let me get this straight. Is the theory of special relativity true?
I mean can mass be changed just by changing its speed close to the speed of light?

Again, it depends on your definition of mass. Relativity discusses what we will observe. If an electron (or proton or whatever) has been accelerated to very nearly the speed of light (c), accelerating it more strongly increases its momentum while its speed hardly changes. Thus its momentum is:

[momentum] = [Lorentz factor] x [rest mass] x [speed]
And its speed = c (nearly)

If we call {[Lorentz] factor x [rest mass]} together simply [mass], one can maintain the classical law:

[momentum] = [mass] x [speed]

Mass is then a measure of its inertia, which is proportional to its energy. However things are less straightforward for gravitation (weight).

See also my post #7 in a recent thread on the same topic:
http://physicsforums.com/showthread.php?t=455698

Cheers,
Harald

[Vanadium 50]

The answer to your firts question is "yes". The answer to your second question is contained in the replies - if there's something specific that you don't understand, that will be more productive than repeating your initial question.

[DaleSpam]

Is the theory of special relativity true?Please see the following and draw your own conclusion:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

I, for one, agree with Vanadium50 that the answer is clearly "yes".

[GrayGhost]

Please see the following and draw your own conclusion:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

I, for one, agree with Vanadium50 that the answer is clearly "yes".

One could look at it in either of these ways ...

the mass increases, with increased speed.

the inertia increases while the mass does not, with increased speed.

I've viewed relativistic mass as the later ...

rest mass + increased relativistic inertia due to motion.

I've always assumed the later, since a collapsing star's mass required to form a black hole is dependent only on the rest mass, and not the state of motion of the observer. Maybe it's just semantics here?

GrayGhost

[DaleSpam]

Maybe it's just semantics here?Yes, it depends entirely on the definition of the word "mass".

[Naty1]

More explained here:
http://en.wikipedia.org/wiki/Relativistic_mass

and in links included in the article.

Note that "relativistic mass" is energy related....so generally today people say that inertia or momentum or energy (as kinetic) increases with increasing velocity.

None of that increase is apparent in the frame of reference of the "body" itself.... where the relative velocity is always zero...

[ApplePion]

<<However, please note that the concept of "relativistic mass" is a bit outdated and, rightly so, being considered to be rather inaccurate>>

In what way is it supposedly inaccurate?

[pervect]

As long as you don't do any of the following with relativistic mass:

calculating momentum using a Newtonian equation involving relativistic mass

calculating a gravitational field using a Newtonian equation involving relativistic mass

assume that relativistic mass is a property of a body that's independent of the frame of reference (which should be obviously untrue!)

you'll avoid most of the usual mistakes.

So, what is relativistic mass good for? Well, it's another name for energy. But that's really better thought of as a component of a larger entity, the combination of energy and momentum into a 4-vector - in my opinion.

Invariant mass, which is a property of the body and the same for all observers (in special relativity), and the energy-momentum 4-vector have mostly replaced relativistic mass in modern treatments. You'll find a few die-hards who still like the relativistic mass concept. To be honest, I'm not sure why.

[gpran]

I wish to mention two views from the forum threads:

A) See thread under Quantum Physics: “Can a grandpa understand the Bell’s Theorem?"

One expert has commented 'Bell's theorem proves that it is not possible to find a classical "explanation" for how QM works except by violating at least one major fundamental principle of physics, for example by using faster-than-light communication.'

Classical mechanics also suggests that photon emitted by a moving source can travel at speed greater than speed of photon emitted by a moving source.

----- Conclusion can be that we have an experiment to support the classical analysis.

B) Theory of special relativity suggests that speed of light is always same and does not depend upon speed of source.

See the thread under relativity: “Einstein’s Theory of Special relativity”.
One expert has replied to question ‘Is the theory of special relativity true?’

Reply is: I, for one, agree with Vanadium50 that the answer is clearly "yes".

----- We can conclude that experiments support the relativity postulate.”

What is the way out to remove this contradiction? Can anybody suggest any
Journal or Book where this issue is discussed in detail? Please guide.

[harrylin]

I wish to mention two views from the forum threads:

A) See thread under Quantum Physics: “Can a grandpa understand the Bell’s Theorem?"

One expert has commented 'Bell's theorem proves that it is not possible to find a classical "explanation" for how QM works except by violating at least one major fundamental principle of physics, for example by using faster-than-light communication.'

Classical mechanics also suggests that photon emitted by a moving source can travel at speed greater than speed of photon emitted by a moving source.

----- Conclusion can be that we have an experiment to support the classical analysis.

B) Theory of special relativity suggests that speed of light is always same and does not depend upon speed of source.

See the thread under relativity: “Einstein’s Theory of Special relativity”.
One expert has replied to question ‘Is the theory of special relativity true?’

Reply is: I, for one, agree with Vanadium50 that the answer is clearly "yes".

----- We can conclude that experiments support the relativity postulate.”

What is the way out to remove this contradiction? Can anybody suggest any
Journal or Book where this issue is discussed in detail? Please guide.

Bell's theorem suggests "Spooky action at a distance". There appear to be several ways out, but the issue is far from settled.

Possibly the two major ways out (which are independent from each other):

1. Accept the possible existence of an absolute reference frame for nature: the theory of relativity is based on operational definitions only, it doesn't say anything about that kind of "metaphysics".
A useful book that discusses that option as well as several others is Tim Maudlin, Quantum Non-Locality and Relativity. You can browse it a little here:
http://www.amazon.com/Quantum-Non-Locality-Relativity-Metaphysical-Intimations/dp/0631232214
Note that that book uses the confusing term "preferred frame". In order to be compatible with relativity, such a physical reference can in no way be "preferred" for our observations.

2. Disagree with Bell's Theorem: it's a rather tricky issue. I just started a thread on a new paper on that topic here:
http://physicsforums.com/showthread.php?t=499002

Harald

[DaleSpam]

I don't know much QFT, but my limited understanding is that QFT is compatible with both Bells theorem and SR. So I don't think that there is a contradiction to be resolved.

[ZealScience]

What about the rest mass? Most of the mass is concentrated in the nucleons, but the mass oringinates mostly from the color force (gluons have more mass than quarks do), when nuclear reaction takes place mass loses correspondingly...

In what I have learnt, the inertial mass is generated by Higgs field, most of the mass is the famous E=mc^2 equation (like photons haven't any inertial mass, but they have pressure due to their momentum) , I am confused by the difference between them. I think in lorentz transformation the mass represents the increase in kinetic energy, exactly the same as other forms of energy...

Just my own view...