Is Energy Conserved?

Classical Mechanics Level 4

There exists a phenomenon in space that explains the red and blue shift observed by astronomers when they look at distant galaxies receding away from us or moving towards us. This phenomenon is more accurately known as the Cosmological Doppler effect .

Imagine a part of the Electro Magnetic spectrum coming to us from a distant galaxy. Since the wavelength and the frequency of this wave change as it moves through space, it can be argued by Plank's hypothesis that the energy i.e. $h\nu$ is continuously changing, or more specifically decreasing, due to the expansion of the fabric of space-time.

So, is it true that it can be said the energy, in this case, is lost?

True False Depends on the wavelength used Depends on the rate of expansion of the Universe.

1 solution

A Former Brilliant Member
Mar 20, 2016

The answer to this hypothesis, as weird as it sounds, is true! I know, it blew my mind away too!

In reality, the laws of conservation of mass and energy are given by something known as the Noether's theorem that derived the Conservation Laws from symmetry, or more importantly it stated that the laws of conservation of energy are the result of an assumption, that laws of Physics don't change over time.

But, from the general theory of relativity and the recent discovery of gravitational waves, we know that the fabric of space time itself can warp, and expand and swivel, hence changing the laws of Physics. So, when a wave passes through space, it causes disturbances, which are enough to violate Noether's theorem and hence the laws of conservation of Energy!

This is actually a complicated subject, and making the claim that "energy is lost" is not a particularly meaningful way to put it. In order to make a meaningful determination of whether or not energy is conserved, it has to be "measured" relative to some inertial frame of reference. But since there is not any such inertial frame of reference for the entire expanding universe, it makes moot the concept of conservation of energy, or whether or not energy is being "lost".

This is an interesting and valuable subject to be talking about, as most have a simplified notion of "conservation of energy".

Michael Mendrin - 5 years, 2 months ago

True! Actually, the concept that you're referring to, i.e. the unavailability of an inertial frame of reference is one of the basic reasons that build up to the concept of Time Invariance, or in other words, time symmetry...that finally lead to Noether's theorem!

A Former Brilliant Member - 5 years, 2 months ago

We can't say that energy is lost. All we can say is that the conservation of energy is not applicable, because we are seeing it from different frames of reference.

Shourya Pandey - 5 years, 2 months ago

I agree, that is what I'm saying.

Michael Mendrin - 5 years, 2 months ago

You can actually say energy is lost! Conservation of energy would be applicable, if you could justify the decrease in energy and where it went!

A Former Brilliant Member - 5 years, 2 months ago

There's the obverse side of the coin. If the "simple" version of the Conservation of Energy Law is not held in a relativistically expanding universe, then we can't so easily say that energy is conserved---which means there could just as easily be an energy gain as well as a loss. Indeed, some folks speculate that's part of the reason why dark energy seems to be increasing. "Where is all this energy coming from?" This is a very confusing subject, and there are now a lot of papers being written about this subject. The conservation of energy law is very difficult to pin down exactly---it works best in "simplified" or local spacetime. Noether's Theorem prescribes those conditions necessary for the law to hold, and you were correct to point out the limited applicability of her theorem and the conservation of energy law. But we need to be careful about exactly what conclusions we could draw from that.

Michael Mendrin - 5 years, 2 months ago

@Michael Mendrin – Agreed, but I have read many papers and saw a couple of vids on this topic as well!

A Former Brilliant Member - 5 years, 2 months ago

@A Former Brilliant Member – The best thing about this topic is that we've already had General Relativity as well as Quantum Mechanics for about a century now, and both of them, when looked closely enough, put cracks in the venerable Conservation of Energy Law. The best way to look at that law is that it applies only when certain conditions are met, but those conditions cannot and should not be assumed to hold anytime anywhere in this universe. That kind of mentality only stunts our deeper understanding of the universe and its laws.

Michael Mendrin - 5 years, 2 months ago

@Michael Mendrin – Very true! I think the only thing stopping us from moving ahead in that field is our inability of not being able to merge QM with relativity. Once, we achieve that feat, it won't be long before we start unravelling the mysteries of the universe and the secrets of the sub-atomic!

A Former Brilliant Member - 5 years, 2 months ago

And can what can be said about momentum? Is it conserved?

Pulkit Gupta - 5 years, 2 months ago

That isn't conserved either, but momentum conservation is not as major of a concept as energy conservation.

According to me, in this case, there is interference from the external causes, like the space time fabric itself, and since momentum is conserved only for isolated systems...so, no.

A Former Brilliant Member - 5 years, 2 months ago

I disagree.

Your reasoning is correct, but it would hold only when I would have explicitly asked if "mechanical momentum is conserved".

Since electromagnetic particles interact via fields, and fields can carry momentum , this lost mechanical momentum appears as the momentum of the field.

Hence, conservation of momentum holds true even for this case.

Pulkit Gupta - 5 years, 2 months ago

@Pulkit Gupta – Uhm...I don't think so. Although I gave my reasoning for mechanical momentum, it kinda holds good for the field momentum, as well.Try figuring it out!

A Former Brilliant Member - 5 years, 2 months ago

I know I'm jumping in quite late, but I'd have to agree that it's a poorly phrased question. In fact, the answer given here would be contrary to the answer given by most cosmologists. The usual idea is that energy is conserved in an inertial frame. However, there are no truly inertial frames in GR. Nonetheless, the idea would be that for some small volume of our expanding universe, we could construct a very close approximation to such an inertial frame. In that frame, observers near one edge are moving with respect to observers near another edge (i.e. comoving volume). Thus the observed red-shift of the photons due to the expansion of the universe is simply the ordinary Doppler shift and thus energy is conserved.

Frank Aiello - 3 years, 9 months ago

Is Energy Conserved?

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