What is all this about infinite mass at the speed of light?

Question

I've seen a lot of people saying that mass nears infinity as you reach the speed of light.

Now to me this all sounds like superstitious hogwash, but then they mention that it involves "special relativity". Honestly to me it sure does sound "special", but more in the mentally challenged sort of way.

Maybe it's just me, but here are the parts I don't understand about this theory:

1) Photons have mass. It has been proven that photons have mass, although the mass seems to vary based on the radiant frequency. A photon's mass is not however infinite, and it travels at the speed of light.

2) Electrons have mass, and it is fairly insignificant. They can be made to travel the speed of light, along with many other particles. In fact if you fire a high power laser through plasma, the particles of plasma will actually get taken for a little ride on the laser beam (at the speed of light) and again, no infinite mass.

So what the heck is all this, a joke?

Infininte mass does not equal infinite volume either. You could have something the size of a grain of sand that had infinite mass, but it would not span all of the universe. Because mass and volume are seperate units of measure.

Maybe I lack some grasp of the obvious as has been suggested.. However I tend to think that the person suggesting this lacks an understanding of the question posed. E=mc^2 means that Energy is equal to the mass times the speed of light squared. Ok, so thats good for figuring out the energy created by an atomic bomb. Then lets balance out the equation and you get m=E/c^2. For infinite mass you need infinite energy.

I can see a the correlation between mass and energy. Mass is energy after all in it's most fundamental bits.

And if photons have no mass, then they have no momentum. Well either that or p=mv is wrong. It seems like everyone is trying to make all of these equations untrue. Without mass you have no momentum. It is part of the very definition of momentum.

And so if you have infinite mass you also have to have infinite momentum, and infinite energy. Heck with all this infinite stuff. The universe will come to an end if something ever goes light speed.. Sheesh.

Photons DO NOT have mass at rest.

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

L(v) = 1/sqrt(1 - v^2/c^2), really?

So I see that if you go the speed of light this equation says that it is all like L(v)=1/0 or basically all indeterminant like.. But um.. if v=c*5 then the equation is unsolvable (can't sqr a negative).

But how does this prove that mass increases at the spead of light? You suddenly throw in there that m=ML(v) so E=ML(v)c^2=mc^2 to make this whole magical mathematic trasformation, but where is the proof? Sure, looks good on paper. But then other things tear this apart.

Say a proton. It is a particle with a rest mass of 0. So from the whole L(v)=1/0 (because they travel at the speed of light). so E=0=mc^2 and therefore photons have no energy... Oh wait, they do? Oops..

While many may believe I am lacking in intellect, or a basic grasp of relativity, I would appreciate a less condescending tone in the answers.

I have said, Photons have no rest mass. And yes indeed, according to modern science photons have no mass. Most of the literature I've read had indicated that photons have mass, but after further research I see that the term was used extremely loosely to try to explain photons in laymans terms.

As far as electrons go, I had misinterpreted a story involving wakefield particle accelerators. Again further research has brought me to fully understand the story.

All I have found in my search though is that relative mass increases with velocity, while mass does not.

So I guess I basically found my answer. It is bunk.. Mass does not increase with velocity. Relative mass does. Which is a different can o' worms. Wish people would clarify their terminology.

Answer 1

Photons have momentum, but no rest mass (M). Their momenta are p = hf/c; where h = Plank's constant, f = frequency of the energy wave packet, and c = light speed in a vacuum. The reason photons can go so fast (c) is because they have no rest mass to increase as their velocity approaches and reaches light speed.

Electrons do have rest mass (M); and they are also energy wave packets that jitter around the nucleus of an atom to form a probability density cloud. The expected value for each cloud is what we call the orbit (based on the old Bohr model), because that's the most likely place the electron will be.

Because they have rest mass, electrons also have momenta due to Mv = P. And because they have rest mass, they are subject to the light speed limits imposed by the increasing mass near light speed.

When we write E = Mc^2, the M is a rest mass found when v = 0. Mass increases with the velocity (v) it is traveling. That increase is determined by the Lorenz transform = L(v) = 1/sqrt(1 - v^2/c^2) accoring to m = ML(v); so that E = ML(v)c^2 = mc^2 is true.

If you look at the Lorenz transform carefully, you can see that it gets to be a very large number at v --> c. When v = c, the transform is an indeterminate some call infinity. This means that the rest mass (M) becomes m = infinity when v = c.

Naturally enough, when m approaches infinity the energy needed to keep it accelerating toward the speed of light also approaches infinity. And there just isn't enough energy in the entire universe to do that last bit of acceleration, which is why all mass is limited in how fast it can go.

Now, to your last point...all this mass thing is not hogwash. Numerous experiments by numerous scientists have over and over proved the Lorenz transform is correct. Mass does in fact increase as it's velocity approaches light speed.

But just what does increased mass mean? Does it mean, for example, that mass is added onto the original, rest mass? Does its size increase? No, not really...what it means is that the rest mass gains more inertia, which is just a resistance to change in position or velocity. It's something like a drag force.

A drag force on a given object is directly proportional to the square of its velocity through air (or gas). That is, the faster the object goes, the more force there is to slow it back down. As a consequence, it takes more and more energy to keep it accelerating through that air or gas. In fact, a free falling body will reach what is called terminal velocity where the drag force exactly equals the body's weight and the acceleration stops...leaving the velocity constant.

Some physicists have proposed the Higgs Field as a kind of multidimensional and still undetected gas that acts on mass in a way similar to the way air acts on a moving body. That is, the faster the mass goes through the field, the more "friction force" acts on it. So at the speed of light, the mass reaches a sort of terminal velocity. Check this out:

"The Higgs field, named after the British physicist Peter Higgs, is a postulated quantum field, mediated by the Higgs boson, which is believed to permeate the entire universe. Its presence is said to be required in order to explain the large difference in mass between those particles which mediate weak interactions (the W and Z bosons) and that which mediates electromagnetic interactions (the photon).

With the next generation of particle accelerators, especially the Large Hadron Collider in Switzerland, which as of 2006 is still under construction, CERN scientists will try to look for particle interactions characteristic of the Higgs Field." [See source.]

The Higgs Field is thought to be directional. If a quantum (like a photon) is aligned with that direction, it has no inertia (no mass). If it is aligned against the direction of the field, it shows inertia and we say it has mass.

Understand, the Higgs Field "direction" is not a direction in ordinary four dimensional space. So the existance of mass or no mass has nothing to do with the velocity of the quantum. But velocity in our four dimensional world does determine the size of that mass according to the Lorenz transformation.

Sure this is weird, but that's what make quantum physics fun.

PS: If you don't want to accept the correct answers, then why bother asking the question? E = Mc^2/sqrt(1 - v^2/c^2) = ML(v)c^2; where M is rest mass and v is the velocity of that mass. The rest mass increases as m = ML(v <= c); where the Lorenz Transform = L(v) = 1/sqrt(1 - v^2/c^2). I repeat, THIS HAS BEEN PROVED OVER and OVER AGAIN by experiments. It not just some theory; it's a proved effect. Look it up on the web.

You said if v = c^5 there would be a negatrive square root...you are absolutely right. But that's proof that v must be <= c, the square root in the Lorenz transform has to be positive and the only way that can be is for v < c. It can't be c^5 as you suggested. By the way, the square root of a negative number yields an imaginary number. You should look that up as well.

Finally, photons do not need inertial mass to have momentum. p = hf/c is a valid and often proved relationship for photon momentum. The fact that photons have momentum is used in the photoelectric cell; its the photon's momentum that knocks out those electrons from the cell.

Answer 2

For someone who has evidently made not much of an effort to understand relativity, you seem very eager to dismiss it all. And very incorrect about everything you said.

1. Photons have no mass, even at rest. As others have pointed out, photons can't really be at rest; they only make sense when traveling at the speed of light.

2. Electrons cannot be made to travel at the speed of light in a vacuum. In many materials, light will propagate at a velocity lower than 'c', and thus in some instances things can travel faster than the local speed of light. Nothing can ever travel faster than the speed of light in a vacuum, which is c.

3. p=mv is a classical formula, thus it is inapplicable to relativistic situations. The relativistic formula you want is E^2 = p^2 c^2 + m^2 c^4. This shows that even a zero mass particle such as a photon can have momentum.

I know relativity can be counterintuitive sometimes... but just because it's not part of our everyday experience doesn't mean that it's superstitious or hogwash.

Answer 3

1) Photons do NOT have mass and cannot exist unless they are traveling at the speed of light. The momentum of a photon is its frequency times the Planck constant. See the source.

2) Electrons DO have mass and can exist at rest. In fact, it is the REST MASS that we mean when we refer to the mass of an electron or any object.

Relativity is not a simple subject. It is NOT intuitively obvious and can only be understood with mind bending math and physics. Unless you are willing to spend a LOT of time and effort to understand the physics and math behind it, you should just ignore it. After all, when was the last time you had any involvement with anything (other than light) that moves at millions of miles per hour?

Answer 4

I answered these exact same questions for another question about the speed of light and what happens with time.

E = m c^2 refers to how much energy any object of rest mass "m" contains WHEN IT IS AT REST. In this form it has nothing to do with motion.

The kinetic energy something possesses is equated at non-relativistic (very low relative to the speed of light) speeds as E = 1/2 m v^2. The formula for speeds closer to light is more complicated, but when you use speeds very low (less than 10% of the speed of light) you get the same formula as I just gave.

Since mass is energy, then as something moves, it gains kinetic energy. This energy IS mass, so the faster something moves, the more kinetic energy it has, and therefore, the more mass is possesses to someone OUTSIDE OF THAT OBJECT'S REST FRAME ENVIRONMENT. An observer from outside would see that the object's RELATIVE mass has increased, but it's spatial dimensions would keep it within the same volume.

Next, photons have no mass. This has been proven repeatedly. Only objects with no mass (photons, neutrinos and a few other particles) can travel at the speed of light. In fact, they HAVE to travel at the speed of light, because to do otherwise, would embue them with something that would be measured as mass. Photon frequencies are based on thier energy and wavelength, but that energy is ALWAYS rest energy. Photons do possess kinetic energy but it is based on the momentum of the photon, which is derived from the Plancke constant and the photon's frequency, not the mass (which is zero).

Electrons have never been made to travel AT the speed of light. Because they have such low mass, they can travel at incredibly high speeds approaching the speed of light, but they, too, are afflicted with the Inifinite Mass issue. An electron can never travel at the speed of light.

NO particle with mass, under ANY circumstances, can travel AT the speed of light.

Answer 5

I'll make it easy for you. E = mc^2 isn't totally correct.
the actual equation is

E = m(final) X c^2,
where
mass(final) = mass(initial) / (SQRT(1 - (v^2/c^2))
where v = velocity

You can see as velocity approaches speed of light, v^2/c^2 approaches 1.

And as this approaches 1, (1 - (v^2/c^2)) approaches 0.

and the SQRT(0) = 0

and as the denominator gets smaller with the numerator staying the same, the total number increases.

And, finally, as the denominator approaches 0, the total approaches infinity.

Now try it. first put in a velocity for v, at some mass mass(inital), then keep increasing the velocity towards the speed of light - you will see that m(final) increases toward infinity.

Answer 6

There are "thing" that can travel a the speed of light: light and gravity You are right, light can't be interpreted as something that has no mass. But what is it then. Einstein famous equation "E=mc^2" tell us that energy and mass are related, different forms of the same thing. Mass is, according to Einstein is a VERY LARGE concentration of energy that can be transformed to a more "direct" form of energy. When you travel to speeds near the speed of light, your mass starts turning into light, the most direct form of energy (again, according to Einstein), and when you finally travel at the speed of light, all your mass becomes light and there is no coming back, light cannot reduce speed. That is why light speed is the "universal" speed limit, because light is the most direct source of energy and travels at that speed!!!!! :O

Answer 7

Your lack of a grasp of the obvious is something you should be quite proud of!

Do the math, the only way this wouldn't be true would be if "E=mc^2" was incorrect; is that what you are trying to suggest?

Try this thought experiment; what would happen to mass (theoretically) if you were able to bring an object's temperature to absolute zero, such that the energy in it was so low, the electrons, neutrons & protons stopped moving altogether? Think of the Bohr model of a simple hydrogen atom in your head, an electron whizzing around a proton & a neutron. How much of that atom is "empty space" and how much is actually 'stuff'?

I think your problem is that you have convinced yourself there is a fundemental difference between mass and energy, and this simply is not true!

Answer 8

when u r in motion u r mass increases with speed.as u keep speeding u r mass will b increasing but at one point or i should say as u reach the speed of light the energy given to accelerate will b simply converted into mass and acceleration will stop at the same speed.in other words energy will not b used to accelerate but only to increase mass and that is infinite mass.but the point is no matter can reach that point

Answer 9

First of all, about "mass" — mass and energy are equivalent, but they are not the same thing. A photon has a "rest mass" of zero (0) plus energy which has a major effect of causing it to move. Other "charge" carriers also have rest masses of zero; in fact, that is one of their main characteristics. When a photon is made more, or less, energetic it is usually called more, or less, massive even though it is wrong to refer to the situation this way because it confuses people no end. Oddly, initially this way was chosen as the standard in order NOT to confuse people (i.e.: so they would not wonder why, if mass and energy are equivalent, that we refer to photon energy and not ever photon mass. Explanations of how semiconductors work using "holes" work well too, except that people go away thinking the created-for-the-explanation holes are real things.).

But to be short about it, mass and energy are equivalent, but not the same. It's a LITTLE like how three pounds of ice and three pounds of steam are very different, yet basically the same thing.

Second, given that, I'll move on to the electrons. They are NOT, in fact, something one can get to travel at the speed of light. For instance, when hit with any light, laser or not, the photons interacting with them are made part of the electrons, raising their energy "content" so they move faster and giving them momentum in the same direction the light was traveling, and then one or more photons are emitted by the electron taking away energy and momentum from it. But at no time did the electron ever travel at the speed of light because...

Third, nothing that is currently NOT traveling at the speed of light can ever be made to speed up to the speed of light. This is implied by Einstein's work because one can see mathematically that to go closer and closer to the speed of light even larger amounts of energy are required (or, equivalently, but not the same, larger amounts of mass) for each tinier and tinier increment of speed. In fact, it is asymptotic and will never quite reach the speed of light because to do so would require an infinite amount of energy to be added and that simply cannot happen. More accurately, that mathematical point is called "undefined" rather than "infinity" as most of us call it, inaccurately. "Undefined" when used mathematically means something a lot closer to "does not exist" than it does "infinity." So, since the solution to Einstein's equations is undefined this way, his work, which has withstood 101 years of scrutiny, says not that it requires infinite energy but rather that it cannot ever happen. By the way, and for the same reason, anything brought into existence moving FASTER than the speed of light can never be slowed down to exactly the speed of light. Not that we know of anything that is moving faster, but if we ever find something...

Fourth, and last, back to mass vs. energy. Though they can be regarded as the same for most things we do with them, they are only equivalent (as in: done somehow correctly, one could be turned into a given amount of the other) and not at all the same. Even the concept of "rest mass" is not perfect as a photon, for instance, NEVER comes to rest. It is always moving at the speed of light in whatever medium it is in whether that be a bath of almost-vacuum space or of ice water or plasma. Speed of light in a bath of energetic electrons is different than in a bath of almost-vacuum in inter-galactic space. So you see the contradiction encased in "rest" of the term "rest mass"? But all non-charge carriers have non-zero rest masses and since they do, they can never have a velocity equal to the speed of light because conditions for them at that velocity are undefined (in the sense of the conditions not even existing, not in the sense of we just have some more work to do), not infinite.

Answer 10

Hi. The simple answer is that mass is resistance to acceleration and the closer you get to 'c' the more resistance you encounter. At 'c' the resistance becomes infinite. We view this as an increase in mass.