Mass vs. Energy

[Mr Spinkles]

Part of the confusion stems from the fact that colloquially (and even sometimes by physicists I suppose) the term "energy" is used to refer to particular forms of what is usually considered "junk" energy, e.g. heat, light, while "mass"--which is also a particular form of energy--is usually still called "mass".

That's why I like Legion's analogy. Quarters, dimes, nickels, and dollar bills are all different. But they all have monetary value and can, in principle, be exchanged for one another. So it is with heat-energy, light-energy, mass-energy, etc.

 

[crossfire]

Ya right! You are a mystic. Only mystics would know stuff like that. :sarcastic

Well, he is a mystic. I cite his making the metaphorical connection between quarters/dollars and energy/mass in a way that imparts understanding as evidence of that.

 

[lewisnotmiller]

in a way that imparts understanding as evidence of that.

I could humbly offer myself as evidence that his methods aren't mystical enough to impart enlightenment on the truly ignorant...

 

[crossfire]

I could humbly offer myself as evidence that his methods aren't mystical enough to impart enlightenment on the truly ignorant...

Oh, do I get to wear my gloves?
Alright....
**wads up a $1 bill, and shoots it with my slingshot at lewis**

That prolly didn't hurt much....

**grabs a $1 coin and shoots it with my slingshot at lewis**

That prolly stung a bit. Obviously, $1 bills and $1 coins have different properties in this respect.

**picks up the $1 bill and the $1 coin and buys beer with it, gives half the beer to lewis, and half the beer to legion**

The beer that the $1 coin can buy is the same as the beer the $1 bill can buy.

Any questions?

 

[lewisnotmiller]

Oh, do I get to wear my gloves?
Alright....
**wads up a $1 bill, and shoots it with my slingshot at lewis**

That prolly didn't hurt much....

**grabs a $1 coin and shoots it with my slingshot at lewis**

That prolly stung a bit. Obviously, $1 bills and $1 coins have different properties in this respect.

**picks up the $1 bill and the $1 coin and buys beer with it, gives half the beer to lewis, and half the beer to legion**

The beer that the $1 coin can buy is the same as the beer the $1 bill can buy.

Any questions?

How come legion's half of the beer looks bigger than mine? Is that related to the theory of relativity?

 

[crossfire]

How come legion's half of the beer looks bigger than mine? Is that related to the theory of relativity?

**shoots a penny at lewis with my slingshot**
That should cover any difference, perceived or imagined.

 

[Curious George]

**shoots a penny at lewis with my slingshot**
That should cover any difference, perceived or imagined.

Everyone knows you are supposed to let one split and the other choose.

 

[crossfire]

Everyone knows you are supposed to let one split and the other choose.

I suppose you're right. **sigh**

**puts Legion's quarters by the beer**

You guys can still have fun playing "quarters" with the beer--that way it won't matter which one has more in it. {if you still have the energy to do so}

 

[Slapstick]

Well, he is a mystic. I cite his making the metaphorical connection between quarters/dollars and energy/mass in a way that imparts understanding as evidence of that.

You must be more of a mystic than I am. I didn't get any that out of the OP.

 

[LegionOnomaMoi]

How come legion's half of the beer looks bigger than mine?

I'm making up for other size deficiencies.

 

[egcroc]

just thinking out loud... during the first physics class I had in school, I learned that the Mass of an object is the amount of matter that object contains, I felt the answer was too shallow, I wondered what matter really was... I had to dig deeper, into the realm of quantum physics, and it turned out that matter is just another form of Energy concentrated in tiny particles that acquire mass by interacting with the Higgs-Boson Field .... which brings up the next big question, What is Energy?!!!!

 

[LegionOnomaMoi]

just thinking out loud... during the first physics class I had in school, I learned that the Mass of an object is the amount of matter that object contains, I felt the answer was too shallow, I wondered what matter really was... I had to dig deeper, into the realm of quantum physics, and it turned out that matter is just another form of Energy

It didn't turn out to be that. Matter is not another form of energy in quantum physics anymore than it is in classical physics. In fact, central to Heisenberg's uncertainty principle is the inverse relation between our knowledge of the momentum & energy vs. position of some quantum "particle", which is akin to saying that energy (like momentum) remains in quantum mechanics as in classical a property of "physical" systems, not equivalent to them.

which brings up the next big question, What is Energy?!!!!

That depends. Potential? Kinetic? Total? Observable representation of? And so on. Mass isn't energy.

 

[Revoltingest]

Yes it's the celebrity death match of the millennium! Ok, no. It isn't. But I remembered not long ago that as a child I was told there are 4 quarters in a dollar. I was very confused because I couldn't feel 4 quarters in any dollar. I didn't understand that saying 4 quarters are in a dollar meant the value of a dollar is equal to that of 4 quarters.

Enter Einstein's Energy-correspondence. Too frequently people get amazed by the fact that energy equals mass (times a constant)! And we get all these statements about how mass and energy are the same and how everything is really one thing and so on all because the famous e= mc^2 equation is so misunderstood. I have tried to explain it by illustrating that energy is also mathematically related to the momentum of massless particles, by talking about what the equation means in terms of systems, by saying we don't equate work and matter or momentum and speed, and so on.

Then I thought of something simpler. Are four quarters the same as one dollar? No. Metal and cloth-like paper are very different and nobody is going to cut a dollar in to four equal pieces and claim they have quarters. But 4 quarters equal a dollar

$.25 * 4 = $1.00

What does this mean!? It means that the value of four quarters is equal to that of a dollars. There's no mystical property about physical quarters that makes them equivalent to a dollar. Just because we can relate things mathematically doesn't mean we are making any ontological equivalences. Mass isn't energy.

I'm a member of BARF (Baptists Against Relativistic Fiziks), & I find your analogy fundamentally flawed.
- 4 quarters have more mass than a dollar bill.
- Your exchange rate is entirely due to a decree by Jewish bankers, & has no mathematical basis.
- No one has ever observed a dollar bill giving birth to a quarter.


Note: No Baptists were harmed in the above post. I like them, & only used their denomination cuz I
needed something starting with "B". (Buddhists & Bahais wouldn't cooperate.) And of course, it seems
there might actually be a few of'm who might really be fundies regarding Newtonian physics.

 

[LegionOnomaMoi]

I'm a member of BARF (Baptists Against Relativistic Fiziks), & I find your analogy fundamentally flawed.
- 4 quarters have more mass than a dollar bill.
- Your exchange rate is entirely due to a decree by Jewish bankers, & has no mathematical basis.
- No one has ever observed a dollar bill giving birth to a quarter.

I always suspected you were secretly a Landover Baptist.

 

[Revoltingest]

I always suspected you were secretly a Landover Baptist.

More of the Bendover variety.

 

[dust1n]

What does this mean!? It means that the value of four quarters is equal to that of a dollars. There's no mystical property about physical quarters that makes them equivalent to a dollar. Just because we can relate things mathematically doesn't mean we are making any ontological equivalences. Mass isn't energy.

Question. How do you add energy to matter?

 

[Revoltingest]

Question. How do you add energy to matter?

- Increase its velocity.
- Increase its temperature.
- Irradiate it. (I'm speculating here.)
- Alter it chemically to be more reactive.
- Increase its pressure.

 

[LegionOnomaMoi]

Question. How do you add energy to matter?

Personally, I use Red Bull and coffee.

More seriously, this depends upon what you mean by "add" and what kind of energy you refer to. The common equations that include energy allow us to see how some system's properties (treated in our model/equation as parameters) are conserved as we allow our system to change over time. In the 1-dimensional case, in which we have some function f that we differentiate with respect to time but do not allow to depend upon time, either the equation is part of a set, we are concerned only with energy, or we can't incorporate energy. Typically, though, we'd be dealing with a 3-dimensional space: x, y, and z coordinates which we treat as degrees of freedom in a model of 6N independent variables. We usually then use Hamilton's equations:

(the dot over the coordinate vector q in the first equation and the momentum vector p in the second indicates we are taking the first derivative with respect to time)

We define the Hamiltonian as follows:

where H is the Hamiltonian function, X is the state vector of some system in Nth dimensional phase space. Then E is the total energy of the system (kinetic and potential). Basically, instead of allowing H to depend explicitly on time we treat it as a constant of motion, differentiating q & p with respect to time for each state j is an index of vectors q & of q.

Or we can ignore all of this and simply realize that changing a system's momentum can increase or decrease its energy.

Things get a lot more dicey when we leave classical physics, but Hamiltonian's do translate fairly readily for both relativistic and quantum physics.

 

[dust1n]

You'll have to forgive my ignorance regarding this matter (pun), but I've never had a physics class before, and I haven't quite got set up for switching schooling to statistics.

So, I'm just trying to get my layman's head around this...

Obviously, 4 quarters and a dollar aren't the same thing. And I guess 90 megajoules and 1 microgram aren't the same thing. But they can convert into each other given some specific circumstances. So, I get the notion that energy and matter aren't the same, but wouldn't there need to be some underlying property to both that allows things to switch back and forth?

 

[LegionOnomaMoi]

You'll have to forgive my ignorance regarding this matter (pun)

Not bad!

So, I'm just trying to get my layman's head around this...

Whoo boy have you gone to the wrong person. My explanations sometimes start out simple and clear, but I end up getting side-tracked by my own thoughts and start thinking about the implications of some aspect of what began as an explanation yet has turned into some exposition or worse.

But they can convert into each other given some specific circumstances

Here's the key part: the values of four quarters and one dollar are equivalent, and we can convert e.g., the value of one temperature from Celsius to Kelvin. Likewise, energies, momentum, mass, etc., are properties of some physical system. Compare a boulder on the top of the hill with the same boulder rolling down. We don't want to describe the boulder as possessing properties such that when it starts rolling down the hill, we end up describing a different boulder. Simply put- we want to "conserve" the boulder by ensuring that whatever properties we use to describe the boulder on the hill, these will only change in ways that describe the boulder as equivalent. So, for example, we know that the kinetic energy of a stationary object is zip, nil, 0. However, when that boulder begins to move, it will have kinetic energy (to test this, find someone you dislike, put them in the path of the boulder, roll it down until it hits them, and then ask if they felt any force from the contact).

Spoiler: Long explanation

Kinetic energy (in classical physics, but how this works in modern physics is analogous enough to use as an example) is simply a function of the objects speed and mass. Force = mass * acceleration (F=ma). When we express this in terms of displacement (net force on a moving body), we wind up finding that we can derive a formula for kinetic energy that gives us the "displacement force" (work done by the net force).

Basically, it tells us that we can express force in terms of a kind of speed (acceleration) and mass, and that when we want to use this to know where a moving object will end up or how much force is required to get it there, we can use the formula for kinetic energy (K=.5mv^2).

Here's the problem: we know that a boulder at the top of a hill has a certain mass and velocity (0 velocity, and therefore 0 acceleration). What's why we don't talk about force for stationary objects, but "work" (simplistically, the amount of force it would take to e.g., get the boulder to start rolling). The boulder also has no kinetic energy. We want to be able to use models (equations) in which we can describe the boulder at the top of the hill and that we can "convert" to describing it falling down the hill at any time t. We have mass, and both force and kinetic energy require that. We even have speed and acceleration (both 0). The problem is that we don't have anything like kinetic energy. We want to talk about the dynamics of the system (i.e., the way our equations change with respect to time as the boulder rolls down the hill), but as is we have to throw in "kinetic energy" as a property of the system that magically appears.

To fix this, we apply the concept of potential energy. Just like work describes a stationary body in ways that are very similar to the force of a moving body, potential energy is a way to talk about the energy of a stationary body like kinetic energy is to moving body.

What we get is conservation of mechanical energy. The boulder on the hill has certain potential energy, kinetic energy, mass, speed, acceleration, etc. (many of these are 0), and will end up having all the same every second it rolls down the hill.

So, I get the notion that energy and matter aren't the same, but wouldn't there need to be some underlying property to both that allows things to switch back and forth?

What switches back and forth are how we describe properties of a system. Mechanics is all about movement (literally). The underlying properties of a dynamical system (a system that changes over time, e.g., increases speed or changes position) include a lot of things that concern dynamics- change. In classical mechanics, these changes are pretty simple: things go faster, they change direction, they stop, they start, etc. Kinetic energy is a way to describe how mass and speed of an object relate to changes in position, while potential energy tells us how a stationary object would need to change for some object to get from point A to point B given a particular mass, speed, etc. It's all about being able to describe some body/system at time t with mass m in ways that allow you to "convert" the values of the stationary object into the moving object the way you would convert Celsius to Kelvin or water into wine (I actually haven't figured out that last conversion yet, but I've heard it was done a while ago by some guy at a wedding).