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How is energy conserved when length contracts?


captcass

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Heisenberg's uncertainty principle tells us that length and energy are related: l * E = ħ / 2 and using natural units where c = 1= ħ, we can deduce that   2*10-16 m = 1 / GeV.

My question is, how is energy conserved when length contracts and time slows? Is it still contained within that smaller space, making the space hotter or is it released in some form? Also, would the slower rate of time have a cooling effect by reducing frequency?

Tks

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5 minutes ago, captcass said:

Heisenberg's uncertainty principle tells us that length and energy are related

Note that this refers to wavelength, not length in general. But your question still applies.

You are right that the energy of a system will depend your speed relative to it. This applies whether you consider the kinetic energy of a massive body or the wavelength of light from a source. Both of these are observer dependent: different people will see different kinetic energy or different wavelength depending on their relative speed.

However, energy is still conserved because it takes energy to change your speed. 

(Note that this gets more complicated once you start considering things like gravitational or cosmological red-shift because the definition of energy, and whether it is conserved, is not simple in GR)

 

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18 minutes ago, Strange said:

You are right that the energy of a system will depend your speed relative to it.

And so mass approaches infinity as  relative velocity approaches c. I would say this is an internal conservation that is observer dependent? In other words, two observers accelerating away from each other in opposite directions would each see each other's mass increase as their size contracted, but not their own?

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5 hours ago, captcass said:

Perhaps does it violate the twin paradox?

OK.......so.......does it eliminate the twin paradox? It would seem "Strange" :) if it did?

Anyone? Hellooo? Getting to be bed time here..........

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15 hours ago, captcass said:

Heisenberg's uncertainty principle tells us that length and energy are related: l * E = ħ / 2 and using natural units where c = 1= ħ, we can deduce that   2*10-16 m = 1 / GeV.

The HUP says nothing of the sort.

Energy and time (not length) are conjugate variables, as are position (not length) and momentum. 

So ∆E∆t > ħ/2 and ∆x∆p > ħ/2

 

 

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10 minutes ago, swansont said:

The HUP says nothing of the sort.

Well spotted. (I assumed he was talking about the Planck relationship and didn’t notice he said “Heisenberg” and got the equation wrong!)

Edited by Strange
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18 hours ago, captcass said:

Heisenberg's uncertainty principle tells us that length and energy are related: l * E = ħ / 2 and using natural units where c = 1= ħ, we can deduce that   2*10-16 m = 1 / GeV.

 

My question is, how is energy conserved when length contracts and time slows? Is it still contained within that smaller space, making the space hotter or is it released in some form? Also, would the slower rate of time have a cooling effect by reducing frequency?

Tks

If the Big Bang were to generate the right amount of helium and other light nuclei, then there must have been an era in the early history of our universe in which light, not matter, made up most of the energy. There were for instance photons around rather than matter. Quantum fluctuations are hypothesised to have initiated the Big Bang. Inflation of the universe could have “stretched” those ancient photons, Doppler-effect-like, some into microwaves, while others kept a higher energy (and kept the possibility to pair produce). A photon can't change its own energy, and for instance change from a gamma ray into an X ray. This is why I support the notion that inflation, the behaviour of the expansion of the early universe, and the presence of more and more dark energy, indirectly changed the wavelength of the photons.

If energy can neither be created nor destroyed, then perhaps life started with quantum fluctuations, but how could these early photons have ever evolved into more and more matter, and eventually into this galaxy we have right now, with a numerous amount of particles? Isn’t this galaxy evidence that there’s no such thing as the conservation of energy? I have two thoughts about this:

1 - Noether’s theorem states that ‘If the laws of physics don’t change with time, energy is conserved’. There’s always a conservation law associated with a specific symmetry. The laws of physics were indeed different before the Big Bang (because there were no laws of physics), the laws changed, so there wasn’t any symmetry law broken that would rule out the quantum fluctuations hypothesis.

2 - Maxwell discovered that the 2nd law of thermodynamics is a statistical law (See ‘Maxwell’s demon’). The 2nd law is a law about probability, unlikeliness, a about statistical impossibility, just like throwing heads instead of tails 1000 times in a row. Violating the 2nd law is a statistical impossibility, which can only be violated with a tiny probability, but on average the 2nd law never decreases.

So, long story short, when you’re stating that “length contracts and time slows”, I'm convinced that there is a high probability (but not a proven certainty) that these processes (inflation + quantum fluctuations) could explain, at least partly, that phenomenon.

Edited by MarkE
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2 minutes ago, MarkE said:

Inflation of the universe could have “stretched” those ancient photons, Doppler-effect-like, some into microwaves, while others kept a higher energy

Expansion (not inflation) has stretched the photons that were around at the era of recombination and they form the cosmic microwave background. (There is no mechanism that I know of for some photons to be unaffected by this.)

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26 minutes ago, Strange said:

Expansion (not inflation) has stretched the photons that were around at the era of recombination and they form the cosmic microwave background. (There is no mechanism that I know of for some photons to be unaffected by this.)

The universe eventually had to cool to 3000 degrees K indeed (in order for electrons to combine with protons, and as a consequence neutral atoms could form), but I was talking about an earlier stage, the (scalar field) inflation, which preceded expansion. The stretching was of course caused by expansion afterwards, thanks!

Edited by MarkE
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1 minute ago, MarkE said:

The universe eventually had to cool to 3000 degrees K indeed (in order for electrons to combine with protons, and as a consequence neutral atoms could form), but I was talking about an earlier stage, the (scalar field) inflation, which preceded expansion.

We can't see any photons from that time. They were all thermalised over the the following 380,000 years.

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4 hours ago, swansont said:

The HUP says nothing of the sort.

I got this from a particle physics book. I am at home, not work, so I can't give yo the title at the moment, but I will provide a link when I get to work..

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I was researching after vsiting this Wiki page on natural units when I found the book.

https://en.wikipedia.org/wiki/Natural_units

I was looking at Planck units when I saw this section at the end and moved on from there.....

"Natural units" (particle physics and cosmology)

In particle physics and cosmology, the phrase "natural units" generally means:[9][10]

ħ = c = kB = 1.

where ħ is the reduced Planck constant, c is the speed of light, and kB is the Boltzmann constant.

Both Planck units and QCD units are this type of Natural units.

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On 3/1/2018 at 12:17 PM, captcass said:

And so mass approaches infinity as  relative velocity approaches c. I would say this is an internal conservation that is observer dependent? In other words, two observers accelerating away from each other in opposite directions would each see each other's mass increase as their size contracted, but not their own?

Actually, no.  While it is common to see it said that mass increases with velocity in many popularizations of SR, modern physics tends to treat mass as an invariant property (this avoids the confusion caused by having to distinguish between rest mass and relativistic mass.  What used to be called relativistic mass is now just included under the label of energy. (with the understanding that some of the properties expressed by mass alone under Newtonian physics are now also expressed by energy.)

So as an object's velocity increases with respect to you its kinetic energy relative to you increases, but if you change your own velocity, your kinetic energy relative to yourself remains 0.

This is no different than for Newtonian physics.  If you collide with a bullet with a relative velocity of several 100's of meters/sec, it doesn't matter if you are at rest with respect to the ground and the bullet was traveling, or the bullet was suspended at rest with respect to the ground and you were traveling with respect to it. The impact between bullet and yourself will be the same, and you will suffer the same consequences.

The difference Between Newton and Relativity is that for Newton the KE increases by the square of the relative velocity and thus approaches infinity only is the velocity approaches infinity, while in Relativity, the KE increases by an asymptotic function and approaches infinity as the relative velocity approaches c.

Length contraction (and time dilation)  result from the fact that observers in relative motion with respect to each other measure time and space along different axis in space-time.( an analogy is to map time as being in the front-back direction and space in the left-right direction. people facing in different directions measure left-right and front-back relative to themselves and differently from each other.   In Relativity, we are dealing with 3 spacial and one time direction and it is relative motion that creates the difference in the space-time axis of the observers.

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20 minutes ago, Janus said:

What used to be called relativistic mass is now just included under the label of energy.

My understanding is that it is just simpler to use the Newtonian formulations, and since relativistic effects only appear at velocities near c, that it just doesn't make a difference in the vast majority of instances. The underlying foundations of Relativity, however, are the basis of our reality.

 

24 minutes ago, Janus said:

two observers accelerating away from each other in opposite directions would each see each other's mass increase as their size contracted, but not their own?

So, is this an accurate statement, then?

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13 minutes ago, captcass said:

My understanding is that it is just simpler to use the Newtonian formulations, and since relativistic effects only appear at velocities near c, that it just doesn't make a difference in the vast majority of instances

It is also a matter of how accurate you need to be.For example, satellite TV receivers don't care about relativistic effects, but GPS receivers have to.

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1 minute ago, Strange said:

It is also a matter of how accurate you need

I am fiddling around with concepts, so prefer the relativistic approach. I am not just trying to solve a problem and looking to use the easiest solution.

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2 hours ago, captcass said:

My understanding is that it is just simpler to use the Newtonian formulations, and since relativistic effects only appear at velocities near c, that it just doesn't make a difference in the vast majority of instances. The underlying foundations of Relativity, however, are the basis of our reality.

 

So, is this an accurate statement, then?

I'm at a loss to how your first statement above relates to the section of my post you quoted.  I was referring to relativistic effects only.  In the early days of Relativity, they used the term "relativistic mass" to refer to the apparent mass increase of a moving object to distinguish it from the "rest mass" of the object or its mass as measured when at rest with respect to the observer.   That term has fallen out of favor.  Today, "mass" is used to mean only the "rest"mass.  "Relativistic mass"  is now just energy which has some "mass equivalent" properties.  Its a matter of convention in terminology to avoid confusion.

 

Thus

Quote

two observers accelerating away from each other in opposite directions would each see each other's mass increase as their size contracted, but not their own?

Is not correct by modern usage of the term "mass" which refers to the "rest mass" which is invariant across reference frames.    The length contraction part is correct because it is reciprocal.

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11 minutes ago, Janus said:

Is not correct by modern usage of the term "mass" which refers to the "rest mass"

OK, I do understand that modern differentiation. So to avoid confusion, let's then just change it to "relativistic mass". Would they also see each other's relativistic mass increase?

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