My understanding of relativity is limited, but as I understand it, the closer something comes to the speed of light the higher it’s mass becomes. Photons can travel at the speed of light because they have no mass. My question is if you could accelerate a single particle with mass (a neutron perhaps, unless there is a better particle to use as an example) to within a vanishingly small percentage of C, could it exceed the mass of the rest of the universe?
If your single particle is moving “within a vanishingly small percentage of C”, what is the speed of the rest of the universe?
I assumed the particles speed would be relative to it’s starting point, so lets say it starts here on earth. As for the speed of the rest of the universe, I don’t know what that is, is there any scientific consensus, or even a theory that is considered most likely?
Yes, a particle’s mass could increase arbitrarily, as you increase its velocity. But to increase a particle’s velocity you need to accelerate it, and to accelerate it you need energy. It would take more energy than exists in the universe to accelerate a particle to where it had a mass greater than the universe. If you got an extra universe worth of energy, then yes you could except you can’t so no you can’t.
Thank you, I knew there was a catch in there somewhere. Anyone else with useful information to contribute please do
I hope the OP forgives me for piggy backing on his question, but:
Can’t the relative velocities of objects in space be extremely high? For example, could the relative velocity between our solar system and a solar system in the andromeda galaxy be something close to c? And if so, wouldn’t the relative masses of both solar system differ significantly BECAUSE of our relative velocities?
I guess what I’m saying is that since everything is always moving relative something else in space, should we be getting some strange mass readings from other objects moving at very high velocities relative to us?
The OP doesn’t mind at all
A particle’s relativistic mass is inversely proportional to the square root of the difference between the speed of light, squared and the particle’s speed, squared.
Note that the denominator goes to zero as s -> c. Hence, the mass -> infinity.
Because of misunderstandings such as your’s physicists have discarded the entire concept of relativistic mass.
Rest mass, real mass, or just mass is equal to the energy of a system that cannot be transformed away. RM can always be transformed away.
If RM were real mass all kinds of weird things would be true:
A single particle traveling close to c could collapse all stellar objects into black holes.
An object would have different masses in different directions.
Mass would wind up being some kind of a matrix function.
Etc.
A neutron’s mighty hard to accelerate - lacking charge, it can’t be hastened along by a cyclotron or whatever. Unless I’m much mistaken, it’s limited to what it got spat out of the nucleus with unless you play one hell of a game of pool. You’re on firmer ground with protons.
Would be a lot more helpful if you explained what misunderstanding you’re referring to. This would involve summarizing the view you believe is a misunderstanding, then giving what you take to be the correct alternative, and offering a diagnosis as to why the misunderstander might have taken the correct alternative to mean something incorrect.
Also helpful would be to explain what you mean by phrases sure to be unfamiliar to many such as “transformed away” and “a matrix function”.
Helpful as well would be to explain what makes the “weird” conclusions you mentioned “weird” in some unacceptable sense. (I mean, we’ve all seen that there is “weird” stuff in correct physics. What makes the “weird” things you mentioned unacceptably weird?)
OP Error:: Mass increases with velocity
Fact :: Mass does not increase with velocity
Transformed away:: Change reference frames
Matrix Function:: If you don’t know what a matrix is you shouldn’t be in this thread-look it up on Wiki
Well if mass increased with velocity a single sub atomic particle traveling close enough to c would collapse the Earth and Sun to black holes, and we all would be dead. Weird enough for you?
So what does happen then? We’re taught in high school physics that mass increases with velocity, if this is wrong what is the alternate proposition? Why does it take infinite energy to accelerate something to light speed?
To a layman this is no more weird than time dilation.
Right. And your helpful diagnosis as to how the OP came to be under this misunderstanding is? What does the OP have right that you can use to help build understanding (or as it’s known around here, “fight ignorance”)?
For sure there’s someone who shouldn’t be in this thread, at least from the behavior exhibited so far.
No, it’s not weird enough for me. How weird would something have to be in order for its weirdness to mean it should be rejected? We can say some pretty “weird” things about Quantum Mechanics as well.
Because relativistic momentum = p = mv/[1 – (v[sup]2[/sup] / c[sup]2[/sup])] [sup]-1/2[/sup]
And relativistic energy squared equals
E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]
So the energy required as speed approaches c goes to infinity
But you’d be dead. An uncountable number of particles travel at close to c.
I respond to polite question politely. I respond to nasty pushy questions in a like manner. This has happened before and I’m tired of it.
You call the above “polite”?
There’s a reason that conversations like this have happened to you before.
The abovequoted is impolite. It’s terse, uninformative (it appears intentionally so) and for these reasons nonconstructive esp considering the purpose of the board.
To open your response with “because of misunderstandings such as yours” without going on to actually explain (not state, but explain) the misunderstanding and the truth of the matter is the opposite of polite.
Being a layman I don’t understand the equations.
Can you please explain why the concept of relativistic mass was discarded? For it be discarded it must have been in use at some point so there must be things about it that were thought of as useful. What part of the concept was good and what was bad? Why was it used in the first place?
I am not a physicist, and this is my understanding of the articles in wikipedia…
An object has a rest mass (also called the invariant mass) - this is the mass of the object from the objects own frame of reference, and it has no relativistic component. Because it is in the objects frame of reference, it is not moving, has no direction, and is a scalar value.
From an external frame of reference, the object has its rest mass, plus relativistic momentum (which is sometimes called relativistic mass). This increases with velocity. However, while it affects the math in the same way as mass (in that increasing the velocity of a relativistic particle requires the same energy as increasing the velocity of a particle with the same rest mass), it is not really the same - momentum (like velocity) is a vector with a direction, not a scalar. There is no limit to relativistic momentum, but it approaches infinity as velocity approaches c. This means that you require infinite amounts of energy to accelerate a particle to c. This is why relativistic momentum (relativistic mass) should not be equated with rest mass - they are different - one has a direction, the other does not. And this was the point Ring was making - if there is no distinction between relativistic momentum and rest mass, then rest mass becomes very complex, and would have to be described by a matrix (not a scalar) and could be different depending on direction. I think that we would notice this.
So the confusion is really the overloading of the term mass, when the vector momentum is a better concept, and the modern approach to teaching derives from this approach. It is just when us laypeople equate rest mass with relativistic momentum and butt heads with physicists that confusion arises.
And this leads me to believe that the answer to the OPs question is no, you could not accelerate a single particle to have the relativistic mass of the entire universe. My logic is thus - in the center of momentum frame of reference for the universe, the vector sum is zero and is conserved. This is invariant, so converting the mass of the universe to energy to accelerate a single particle cannot be done, as this would create a single non-zero momentum vector. The best you could do would be two particles with opposite vectors, each with a relativistic momentum of half the universe rest mass (and nothing else in the universe). But … I may be wrong. :smack:
Si
I seem to remember an article by John Baez from a while ago, that did a very good job of explaining the concepts of ‘relativistic’ and ‘invariant’ mass. Trouble is I either can’t find it or don’t remember it correctly. I distinctly recall it came down strongly against the idea of relativistic mass (as did all my lecturer back when I did physics umpty years ago). However the link I get most frequently in google is this one which appears to defend the concept! I also get this which might be very illuminating if I could get past the terrible equation rendering.
Here’s my rusty take on it. In Newtonian Mechanics, mass is invariant, momentum=p=mv, and force=f=ma (rate of change of momentum with time).
In special relativity, something has to change, and there’s disagreement about how to do it. One way is to say that an object’s mass does indeed depend on its velocity in a given frame of reference. Thus we talk about the ‘rest mass’ m_0 which is invariant, and the ‘relativistic mass’ m_r=m_0/sqrt(1-v^2/c^2) (and I talk about someone else’s terrible equation rendering…) which goes up as an object’s velocity goes up, and tends to infinity as the object reaches speed c. In this case, we can keep the old definition of momentum, p=mv, just as long as we realise it’s the relativistic mass m_r that goes in there.
The way that appears to be preferred nowadays is to ignore the concept of relativistic mass, just talk about the ‘invariant’ mass, and change the definition of momentum to read p=mv/sqrt(1-v^2/c^2). This is how I was taught to regard things, and I am convinced by the (possibly misremembered) argument I heard. Basically, mass plays two roles in physics. It is inertia (how hard it is to change an object’s state of motion) but it is also ‘gravitational charge’ (how much gravity an object produces and feels). You can get away with velocity-dependent inertia, but not velocity-dependent gravity… an object’s gravitational field depends on its invariant mass, and does not increase with velocity. So it makes sense to discard relativistic mass and just use the modified equation for momentum.
(and FTR I saw nothing impolite about Ring’s reply, I think Frylock is taking things a bit personally)
Thanks si.
I don’t think Ring’s reply was impolite but it was unhelpful. He apparently has the knowledge to give an answer like si blakely’s but didn’t, even when asked to expand.