Energy is the conserved quantity associated to time-translation invariance and represents the work a system is capable of doing. Use this tag for questions about energy, and consider adding [tag:energy-conservation] if it is specifically about its conservation.

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48
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8answers
11k views

Why does holding something up cost energy while no work is being done?

I read the definition of work as $$W ~=~ \vec{F} \cdot \vec{d}$$ $$\text{ Work = (Force) $\cdot$ (Distance)}.$$ If a book is there on the table, no work is done as no distance is covered. If I ...
78
votes
16answers
21k views

Why does kinetic energy increase quadratically, not linearly, with speed?

As Wikipedia says: [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $mv^2/2$. Why does this not increase linearly with speed? Why does it take so much ...
18
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2answers
3k views

Black holes and positive/negative-energy particles

I was reading Brian Greene's "Hidden Reality" and came to the part about Hawking Radiation. Quantum jitters that occur near the event horizon of a black hole, which create both positive-energy ...
39
votes
6answers
2k views

What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
45
votes
12answers
15k views

What happens to the energy when waves perfectly cancel each other?

What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be ...
9
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3answers
1k views

Explain how (or if) a box full of photons would weigh more due to massless photons

I understand that mass-energy equivalence is often misinterpreted as saying that mass can be converted into energy and vice versa. The reality is that energy is always manifested as mass in some ...
28
votes
4answers
11k views

Why can't energy be created or destroyed?

My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or ...
11
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2answers
2k views

Does $E = mc^2$ apply to photons?

Photons are massless, but if $m = 0$ and $E=mc^2$, then $E = 0c^2 = 0$. This would say that photons have no energy, which is not true. However, given the formula $E = ℎf$, a photon does have energy ...
46
votes
7answers
16k views

What Is Energy? Where did it come from?

The simplistic undergrad explanation aside. I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind does some ...
21
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4answers
5k views

Amplitude of an electromagnetic wave containing a single photon

Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?
14
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4answers
6k views

When is the Hamiltonian of a system not equal to its total energy?

I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
11
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6answers
2k views

Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?

For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$ \frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$ From this, it ...
15
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3answers
3k views

How does rest mass become energy?

I know that there's a difference between relativistic rest mass. Relativistic mass is "acquired" when an object is moving at speeds comparable to the speed of light.Rest mass is the inherent mass that ...
1
vote
2answers
252 views

How can gravity affect light?

I understand that a black hole bends the fabric of space time to a point that no object can escape. I understand that light travels in a straight line along spacetime unless distorted by gravity. If ...
1
vote
2answers
398 views

Is light affected by gravity? Why?

I would like to know if light is affected by gravity, also, I would like to know what is the correct definition of gravity: "A force that attracts bodies with mass" or "a force that attracts bodies ...
13
votes
7answers
2k views

Can energy be taken out of the QFT vacuum?

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
35
votes
7answers
17k views

Is a hard drive heavier when it is full?

Browsing Quora, I saw the following question with contradicting answers. For the highest voted answer: The bits are represented by certain orientations of magnetic fields which shouldn't have ...
16
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4answers
792 views

Redshifting of Light and the expansion of the universe

So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light ...
6
votes
3answers
430 views

How do photons know they can or can't excite electrons?

This might be a stupid question, but nonetheless, it has been bothering me. If you take a photon, make it go through some atoms in a solid, liquid or whatever, then you have the chance of this photon ...
3
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5answers
3k views

Is the law of conservation of energy still valid?

Is the law of conservation of energy still valid or have there been experiments showing that energy could be created or lost?
9
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4answers
9k views

Why is energy in a wave proportional to amplitude squared

I'm a mathematics student trying to grasp some basics about wave propagation. A sentence I find very often in introductive physics textbooks is the following: In a wave, energy is proportional to ...
7
votes
4answers
7k views

What is the pure energy in matter antimatter annihilation made of?

I used to read the term "pure energy" in the context of matter antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass ? ...
-2
votes
3answers
945 views

Anti-laser: How sure we are that energy is transported?

Reading this PE question can-we-transport-energy-over-infinite-distances-through-vacuum-using-light, a related question arises naturally: Is energy transported (by light)? -- (I did believed in this ...
6
votes
4answers
386 views

Is $E^2=(mc^2)^2+(pc)^2$ correct, or is $E=mc^2$ the correct one?

I have been having trouble distinguishing these two equations and figuring out which one is correct. I have watched a video that says that $E^2=(mc^2)^2+(pc)^2$ is correct, but I do not know why. It ...
19
votes
6answers
29k views

Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?

I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ...
6
votes
3answers
251 views

Is energy content of a system different dependending on the observer?

For the sake of simplicity, let's imagine that the entire Universe is empty except for a single lump of (classical) matter with mass $m$. In its center of momentum frame, it is clear that the total ...
61
votes
10answers
8k views

What makes running so much less energy-efficient than bicycling?

Most people can ride 10 km on their bike. However, running 10 km is a lot harder to do. Why? According to the law of conservation of energy, bicycling should be more intensive because you have to ...
12
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5answers
5k views

Is the total energy of the universe constant?

If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
16
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2answers
867 views

If energy is only defined up to a constant, can we really claim that ground state energy has an absolute value?

Sorry if this is really naive, but we learned in Newtonian physics that the total energy of a system is only defined up to an additive constant, since you can always add a constant to the potential ...
8
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3answers
2k views

Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in e=mc^2. Maxwell's Demon can turn information supplied ...
20
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9answers
12k views

Why is torque not measured in Joules?

Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$. This means the units of torque are Newton meters. Energy is also measured in Newton meters which are ...
4
votes
2answers
1k views

Is the E-cat by Andrea Rossi et al. for real?

Does this thing really do what they say? http://www.youtube.com/watch?v=EhvD4KuAEmo If it does, it looks like this will probably be the biggest breakthrough in science ever :)
5
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2answers
3k views

Conservation of Energy in a magnet

When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply ...
6
votes
8answers
17k views

How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
6
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2answers
432 views

What is the percentage of useful energy do we get from matter-antimatter annihilation?

This is a theoretical question since we haven't made enough antimatter to try it in reality of course. But I am asking about the physics part in this. Also, by "useful energy" I mean the energy we ...
27
votes
4answers
1k views

Are there any theoretical limits on the energy of a photon?

Is there any lower or upper limits on the energy of a photon? i.e. does the mathematical framework we currently use for Quantum Mechanics blow up when a photon surpasses a certain upper limit of ...
22
votes
5answers
3k views

Do photons gain mass when they travel through glass?

Please correct me if I'm wrong, but I believe that photons slow down when travelling through glass. Does this mean they gain mass? Otherwise, what happens to extra kinetic energy? I understand now ...
6
votes
5answers
720 views

Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
5
votes
3answers
507 views

Cosmic ray hazards

The Pierre Auger Observatory site mentions the detection of a 3E20 eV (48 J) cosmic ray whose energy, well above the GZK cutoff, was based on an analysis of its atmospheric shower. This was equivalent ...
12
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7answers
14k views

How efficient is an electric heater?

How efficient is an electric heater? My guess: greater than 95%. Possibly even 99%. I say this because most energy is converted into heat; some is converted into light and kinetic energy, and ...
5
votes
3answers
1k views

How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?

The world is full of nuclear warheads being stockpiled. Controlled fusion power seems a long way away. Could we put these warheads to better use by exploding them in a controlled way and capturing ...
4
votes
6answers
12k views

Is fire matter or energy?

I wanted to know that if FIRE is Matter or Energy. I know that both are inter-convertible. but that doesn't mean there is interconversion taking place just like nuclear fusion or fission. If it is ...
2
votes
2answers
313 views

Travel at the speed of light

Is it me who have a poor understanding, or does all matter have to become 'pure energy' in order to achieve speed-of-light speed? If so, does that mean that no material can achieve the speed of ...
2
votes
4answers
483 views

Conversion of mass and energy

First of all I am not a scientist and all these doubts are coming from my curiosity. When Googling about Einstein's $E = mc^2$. I understand that mass and energy are convertible. What it exactly ...
29
votes
4answers
4k views

What's the real fundamental definition of energy?

Some physical quantities like position, velocity, momentum and force, have precise definition even on basic textbooks, however energy is a little confusing for me. My point here is: using our ...
18
votes
7answers
2k views

How was the formula for kinetic energy found, and who found it?

My questions mostly concern the history of physics. Who found the formula for kinetic energy $E_k =\frac{1}{2}mv^{2}$ and how was this formula actually discovered? I've recently watched Leonard ...
10
votes
3answers
2k views

What are the calculations for Vacuum Energy?

In wiki the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in Quantum Electrodynamics (QED) and Stochastic ...
5
votes
2answers
977 views

Energy operator

Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...
10
votes
3answers
632 views

Where's the energy in a boosted capacitor?

Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$. Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
7
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2answers
1k views

Photon energy - momentum in matter

$E = h\nu$ and $P = h\nu/c$ in vacuum. If a photon enters water, it's frequency $\nu$ doesn't change. What are its energy and momentum : $h\nu$ ? and $h\nu/c$ ? Since part of it's energy and momentum ...