Trying to understand E=mc2 here !!!!!!!

[worship4ever]

Hello all, i some 2 real quick questions on E=mc2.
I understand that all matter is just a form of energy, and you can't reach the speed of light because you'll never be able to accelerate a mass that speed cause you would never have the amount of energy needed.
My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?
Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.
Thanks guys, and if you could, explain in lamems terms, heck, ever try to give an example if needed, lol. Thanks again.

 

[michabo]

worship4ever,

If you ask on the science forum, you will likely get much better answers, but I'll try my best.

I understand that all matter is just a form of energy, and you can't reach the speed of light because you'll never be able to accelerate a mass that speed cause you would never have the amount of energy needed.

The relativistic mass goes to infinity, so the energy required to accelerate grows exponentially. It is an asymptotic curve, never reaching c.

My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?

Good question, with a difficult answer. I suppose the answer is the the object doesn't gain mass, but that observers with different relative motions observe different masses (just as they will observe different lengths and different rates of time). It is the difference in speed which is important. A lengther discussion of this can be found here and here.

Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.

Hmm... there's a brief discussion here.

In short, imagine a space ship with a clock which is built using a photon which bounces between two mirrors. Each time it bounces off a mirror is a tick. Now imagine what happens when you look at this clock as it goes moving past you at some significant fraction of c. Instead of going straight up and down, each photon follows a zig-zag path. That is, the distance required to travel for each tick grows longer and longer as the ship goes faster and faster. So if a tick used to take time 't', now it is taking 2t. As the ship goes faster, the distance grows longer, so takes 3t, 4t, 5t, and so on.

Notice that if you were in the ship, you would not see any difference and time would be moving at the same rate as you expect. Notice also that if you look at the clock of the "stationary" observer (who would be moving relative to the space ship), you would see his clock moving slower, too.

Make a kind of sense?

 

[WaZoO]

E=(mc^2) / (1 - v^2 / c^2) is the expanded form...

As v approches c, the denominator approches 0, and m and E approch infinity. I think...

edit: oops michabo provided a way better answer.

I'll leave this just incase it's right

 

[Qingu]

Another way to look at relativity is that "distance" and "time" are defined by the speed of light, not the other way around (since the speed of light is constant, and distance and time are not constant).

 

[Magisterium]

My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?

Matter gains mass when enery is applied to it and conversely loses mass when energy is extracted from it. For instance, when thermal energy is removed from matter (like when it's frozen) it's mass decreases (even though water's volume increases, it's mass still decreases). This can also be seen in systems like rechargeable batteries. (a fully charged one generally weighs more than a discharged one).

Likewise, when matter is accelerated, kinetic energy is added to it. Kinetic energy like electrical and thermal accounts for additional mass when applied to matter.

Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.

Well, first of all, time logically constructed unit of measure. Time measures change according to a scale comprised of seconds, minutes, hours, etc.

That said, time itself is not variable. It cannot really slow or speed up. What happens as one theoretically approaches the speed of light, is that more and more work can be done in a finite span of time. This rapid change means that the "scale" of time appears to be altered because the amount of change that is normally contained within a second is increased.

It really no different than the following scenario:
Let's say that Bob works at a factory making clocks. In an 8 hour day, Bob can usually churn out 10 clocks.

If We accelerate Bob's activity rate to double the normal, he might be able to produce twice as many clocks. It appears to Bob's supervisor that time must have slowed because Bob's output is greater than is normally possible given that space in time (8 hours).

Hope that helps...

 

[michabo]

For instance, when thermal energy is removed from matter (like when it's frozen) it's mass decreases (even though water's volume increases, it's mass still decreases). This can also be seen in systems like rechargeable batteries. (a fully charged one generally weighs more than a discharged one).

What the...?!? What are you talking about?

The amount of "mass" which is stored in a battery's potential energy while charged is a fraction of an atom. To claim that a battery "generally weighs more" while charged is a gross misstatement. Similarly, to claim that frozen water weighs less is a gross misstatement. Have you ever tried plugging in values into E=mc^2? It looks deceptive, but that c^2 is a huge factor, so even millionth of a gram becomes an enormous amount of energy. The amount of energy gained or lost while freezing or thawing is not detectable through a change of mass.

Kinetic energy like electrical and thermal accounts for additional mass when applied to matter.

No. That is to say the change is in such miniscule amounts your scales would have to be calibrated to measure single atoms.

That said, time itself is not variable. It cannot really slow or speed up. What happens as one theoretically approaches the speed of light, is that more and more work can be done in a finite span of time. This rapid change means that the "scale" of time appears to be altered because the amount of change that is normally contained within a second is increased.

Again, totally wrong.

Time may be affected just as our speed through space may be sped up or slowed down. If you wish to be totally accurate, you could say that the magnitude of the four-vector representing our motion through space and time is always equal to c, so when an observer sees us as moving through space, they would see us moving through time less quickly. We do not see our own clocks change as we are generally stationary (we'll leave the case of accelerated motion out of this for the moment).

If We accelerate Bob's activity rate to double the normal, he might be able to produce twice as many clocks. It appears to Bob's supervisor that time must have slowed because Bob's output is greater than is normally possible given that space in time (8 hours).

That's nothing like what is observed in SR. With time dilation, both parties observe the other as slowing down. In your example, bob is clearly going faster.

 

[Aeschylus]

Hello all, i some 2 real quick questions on E=mc2.
I understand that all matter is just a form of energy, and you can't reach the speed of light because you'll never be able to accelerate a mass that speed cause you would never have the amount of energy needed.
My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?
Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.
Thanks guys, and if you could, explain in lamems terms, heck, ever try to give an example if needed, lol. Thanks again.

Deriving mass-energy equivalence, is not a particaulry simple task and to undersdtand the derivation you need more than a layman's understanding of the principles involved, so I won't do it here. Time dialtion can be demosntarted by much simpler arguments (Michabo has alreday posted the classic 'light clock' example which is by far the easiets to understand). Historically scienitsts first discovered these phenoumena from the two postulates of special relativity which are that the laws of physics are the same for all (inertial) observers and the speed of light is the same for all (inertial) observers.

Time dialtion is relative so lets say I'm travelling away from you at 0.9c, from your pount of view my 'clock' is running slow, but from my point of view it is you who is moving away at 0.9c so your clock is running slow.

Once you bring in accelartion into relativty it gets alot more complicated as the two postulate sof relativty do not apply to accelerated observers



Note: The full equation is E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup] (where p is the 3-momentum)

What this equation is actually saying is that m DOES NOT CHANGE with velcotiy (it's the length of the four momentum vector, i.e. we can re-write the equation as m[sup]2[/sup] = p[sup]μ[/sup]p[sub]μ[/sub], taking c as 1).

But what you can do is is to put the equation into the form of: E = γmc[sup]2[/sup] where γ = (1 - v[sup]2[/sup]/c[sup]2[/sup])[sup]-1/2[/sup], you cna then define a new quantity M = γm ('M' is called the 'relativstic mass' and is an outdated concpet due tot he way that relativty is formulated today, but it does have some of the qualitiesof Netwon's defintion of mass) and then you can write E = Mc[sup]2[/sup]. Clearly M is dependent on velocity (v).

 

[UnhandledException]

Imagine two objects flying towards each other. For example, a child throws a ball at a car. If the car is moving at 30 mph and the child throws the ball at 10 mph in the opposite direction, then when the ball hits the car, the ball will “feel” like it’s moving 40 mph. The speeds are additive. Similarly, if the child throws the ball at the rear of the car as it is moving away, the speeds are subtractive. If the child throws a ball at 40 mph at a car moving away at 30 mph, the ball will “feel” like it was going 10 mph when it hit the car. All this makes sense, right? Well, light doesn’t work that way. If I gave you the same example as above, only using light instead of a ball, all the answers above would be equal to c (the speed of light). Light has no relativity like other objects. Now, in order for our little brains to comprehend this, scientists have come up with an explanation. If speed is relative to time and we all know that speeds are additive (see ball example above) time must shrink in order for the light example to make sense. If time shrinks; you use a different time for the light then for the car, then it all works out.



I have a better explanation. When God created the Universe, He needed a constant to base everything off of. I believe He chose light for this.

 

[Arkanin]

My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?
Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.

If you are asking for a mathematical explanation of these things, this can be done. But if you are looking for some transcendental justification for why our world works the way it does, the best and brightest mathematician in the world can't do more than just shrug his shoulders and say 'just because that's how it works and past that, I don't know'.

 

[RVincent]

Close, but you're ALL wrong.

E=mc² is the formula equation developed by Yahoo Serious for putting bubbles into beer.

 

[Dragar]

My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?

I think you need to stop considering mass as being some fundemental 'thing'. Just think of it as a property, like temperature or kinetic energy. In fact, you can start to think of mass as just another form of energy. That's one of the things E = m(v)c² means.

Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.

As a very, very simple conceptual aid (which has a great many flaws, but may help you think about this): imagine we are all travelling along spacetime (that's four dimensions) at a speed of c. Constantly. Everything is always moving at c along spacetime. As we move faster and faster along the spacial directions, our velocity along the temporal part tends to 0.

Dragar

 

[worship4ever]

People, great thoughts here. I'm loving the discussion, but lets put this stuff into an application, give examples. But, what im getting here, is that time nor matter increases with accerlation, only the idea of it? Am i kinda right?

 

[michabo]

But, what im getting here, is that time nor matter increases with accerlation, only the idea of it? Am i kinda right?

Let's say that the observed rate of time and the observed mass varies with velocity relative to a "stationary" observer ("inertial frame"). It really does change; this isn't just a notion. We have done experiments and validated the predictions, it is a real effect.

 

[freak_of_today]

Close, but you're ALL wrong.

E=mc² is the formula equation developed by Yahoo Serious for putting bubbles into beer.

So that's what my physics teacher was getting at when he triend explaining this to us....

 

[Dragar]

People, great thoughts here. I'm loving the discussion, but lets put this stuff into an application, give examples. But, what im getting here, is that time nor matter increases with accerlation, only the idea of it? Am i kinda right?

Not acceleration (that's general relativity, and more advanced) - relative velocity to the observer.

Here's an example of how energy and mass are interchangable: a neutron which is bound in a nucleus has a certain binding energy. This energy is the energy you'd need to pull it apart from the nucleus.

The mass of a free neutron is different to that of a bound neutron. And the mass difference, if converted into energy by E = mc², is precisely the binding energy.

This is a real effect.

Dragar

 

[ronaldp]

Hello all, i some 2 real quick questions on E=mc2.
I understand that all matter is just a form of energy, and you can't reach the speed of light because you'll never be able to accelerate a mass that speed cause you would never have the amount of energy needed.
My question is: How can matter GAIN mass while its being accelerated. What is it about accelerated that actually allows matter gain mass?
Also, how can time be slowed down while accelerating toward the speed of light? I understand its all relative, but why does time slow the closer you get toward the speed of light.
Thanks guys, and if you could, explain in lamems terms, heck, ever try to give an example if needed, lol. Thanks again.

Hi, I'm not really good at this but I'll try to explain it the best way I could. Well here it goes, Matter doesn't gain energy, the energy was already inside it. For example a nucle bomb, how can a small thing destroy miles and miles of civilization. Energy is already inside matter, they are condensed and it's just that we haven't found the technology to harnest that energy. According to the theory of relativity a single penny can power the whole U.S for 70 years, that's because in matter the energy is just big but condensed into a small matter and wouldn't be able to get released until you have bombarded them with each other at the speed of light. For me, I don't think time slows down when we get closer to the speed of light, because time still goes on normally, but it's just the object traveling faster. For example, when you drive towards home and home is 60 miles away ok. When you drive 60 miles you will reach your home in an hour, but when you drive 120 miles per hour then you will reach your home in 30 minutes. It's not that time slowed down it's just that you're reaching your destination at a shorter time, because you are fast. I think that time doesn't stop when you go at a speed of light or time goes backward when you go faster. I think time still moves forward when you reach the speed of light or go faster than the speed of light. This is my reasoning as you get closer to a speed of light your denominator get closer to zero right, well it never actually reaches zero, it goes to like 0.000000000001 I think, it never actually reaches zero, but according to physics you might as well round it off to zero, but when you round it off to zero then it seems that time is stopped because you can't divide when the denominator is zero right, but when it's not rounded off then time is not actually stopping or time goes backward when you go faster because the denominator is not actually zero infact the result will be bigger than the numerator. Rounding the denominator changed the whole outcome. Well the whole theory of time not actually stopping is actually my opinion of the theory.

 

[Aeschylus]

People, great thoughts here. I'm loving the discussion, but lets put this stuff into an application, give examples. But, what im getting here, is that time nor matter increases with accerlation, only the idea of it? Am i kinda right?

The problem is what you are asking is to ill-defined. What we can say is that different observers observer different amounts of time between two events and you cdifferent obsrevers observe different relativstic masses.

 

[Aeschylus]

Not acceleration (that's general relativity, and more advanced) - relative velocity to the observer.

Special relativty can deal with accelartion can deal with accelartion (if you do a course in relativty you will come across the concept of 4-accleration, an object that is acclerateing has a curved worldine) and accelarted refernce frames (this fact is actually less widely known, I even remebr reading a column by an MIT cosmologer wghere she asserted that special relativty can't deal with accelarted refrence frames. The reason for this probaly thta the two postulates of SR don't apply to acelarted refrence frmaes, but that's no biggie, to comapre not all of Newton's laws of motion apply to accelarted refrence frames in Newtonian physics).

Depending on how much maths and physics you've done, this explantion may or may not make sense:

Accelarting frames in SR can be much more diffcult as the first postulate of relativty (i.e the laws of physics are the same in any inertoial frame) does not apply so we essientally have to work out the laws of physics for the frma eunder consideration. At any instant of time an accelarting object is in an inertial frame (which correponds to the tnagent vector to it's worldine i.e. it's four velcoity) which is called it's momentarily co-moving inertial frame, by integrating over an accelarting object's MCIFs, we can work out without too much trouble simple things like the amount of time between two event sthat an objects. In more adavnced geometrical treatments by clever choicing the right basis (and therefore altering the form of our metric) we can talk about spacetime in terms of curvilinear coordinates, this is infact very simlair to delaing with accelartion in GR against a flat background.

 

[Aeschylus]

Hi, I'm not really good at this but I'll try to explain it the best way I could. Well here it goes, Matter doesn't gain energy, the energy was already inside it. For example a nucle bomb, how can a small thing destroy miles and miles of civilization. Energy is already inside matter, they are condensed and it's just that we haven't found the technology to harnest that energy. According to the theory of relativity a single penny can power the whole U.S for 70 years, that's because in matter the energy is just big but condensed into a small matter and wouldn't be able to get released until you have bombarded them with each other at the speed of light. For me, I don't think time slows down when we get closer to the speed of light, because time still goes on normally, but it's just the object traveling faster. For example, when you drive towards home and home is 60 miles away ok. When you drive 60 miles you will reach your home in an hour, but when you drive 120 miles per hour then you will reach your home in 30 minutes. It's not that time slowed down it's just that you're reaching your destination at a shorter time, because you are fast. I think that time doesn't stop when you go at a speed of light or time goes backward when you go faster. I think time still moves forward when you reach the speed of light or go faster than the speed of light. This is my reasoning as you get closer to a speed of light your denominator get closer to zero right, well it never actually reaches zero, it goes to like 0.000000000001 I think, it never actually reaches zero, but according to physics you might as well round it off to zero, but when you round it off to zero then it seems that time is stopped because you can't divide when the denominator is zero right, but when it's not rounded off then time is not actually stopping or time goes backward when you go faster because the denominator is not actually zero infact the result will be bigger than the numerator. Rounding the denominator changed the whole outcome. Well the whole theory of time not actually stopping is actually my opinion of the theory.

No object with a refrence frame can travel at or above the speed of light in any inertial refrence fram eso special relativty says nothing about this. Remember that speed is relative not absolute o 'time slowing' is an eefcet seen by obsrevers whose relative speeds are a frcation of the speed of light.

 

[Dragar]

Special relativty can deal with accelartion can deal with accelartion (if you do a course in relativty you will come across the concept of 4-accleration, an object that is acclerateing has a curved worldine) and accelarted refernce frames (this fact is actually less widely known, I even remebr reading a column by an MIT cosmologer wghere she asserted that special relativty can't deal with accelarted refrence frames. The reason for this probaly thta the two postulates of SR don't apply to acelarted refrence frmaes, but that's no biggie, to comapre not all of Newton's laws of motion apply to accelarted refrence frames in Newtonian physics).

Ah. My many thanks, Aeschylus.

Depending on how much maths and physics you've done, this explantion may or may not make sense:

Accelarting frames in SR can be much more diffcult as the first postulate of relativty (i.e the laws of physics are the same in any inertoial frame) does not apply so we essientally have to work out the laws of physics for the frma eunder consideration. At any instant of time an accelarting object is in an inertial frame (which correponds to the tnagent vector to it's worldine i.e. it's four velcoity) which is called it's momentarily co-moving inertial frame, by integrating over an accelarting object's MCIFs, we can work out without too much trouble simple things like the amount of time between two event sthat an objects. In more adavnced geometrical treatments by clever choicing the right basis (and therefore altering the form of our metric) we can talk about spacetime in terms of curvilinear coordinates, this is infact very simlair to delaing with accelartion in GR against a flat background.

That made a great deal of sense; thank you greatly! I may look into this; we do far too little relativity for my tastes.

Dragar