# I Spacetime expansion and conservation of energy

1. May 2, 2016

### EasterEggs123

I came across this issue a while ago, when spacetime expands, then energy doesn' seem to be conserved? But does not that violate the law of conservation of energy? I don't get it, how can spacetime expansion happen without energy issues? Thanks in advance

2. May 2, 2016

### PabloAMC

Could you be more specific about why you think this is a contradiction? You must take into account that space-time is deformed according to general relativity due to the presence of mass, and therefore it involves energy.

3. May 2, 2016

### EasterEggs123

Well the wavelengths of photons (CMB) get stretched but the number of them is the same.

4. May 2, 2016

### Staff: Mentor

This is actually a complicated issue and depends on what you mean by "energy" and "conserved". There's a good link that explains it that I'll try to find.

5. May 2, 2016

6. May 2, 2016

7. May 2, 2016

### George Jones

Staff Emeritus
A huge truck that whizzes by me has loads of kinetic energy. I get on my bike and pedal so furiously that the truck has no relative velocity with respect to me, and thus zero kinetic energy. Where did the energy go? Nowhere, I changed frames of reference. Using a non-rigorous analogy, we continuously change frames of reference as the universe expands.

Mass-energy is, however, always conserved locally in general relativity. More technically, the 4-dvergence of the stress-energy tensor is zero.

8. May 2, 2016

### EasterEggs123

Apologize if I sound like a high schooler (because I am) but would not the acceleration of our bike be equal to usage of energy? Would it not take energy to change the frame of reference, which is supposed to explain the energy issue?

9. May 2, 2016

### George Jones

Staff Emeritus
Because of this possible confusion, I carefully chose the two vehicles. Suppose that initially you and I are are stationary with respect to the ground. You remain stationary. After I start pedaling, you see: 1) the truck and me moving with the same speed; 2) the kinetic energy of the truck to be much larger than the kinetic energy of the bike/me system bike, because the mass of the truck is so much larger. The gain that you see for my kinetic energy is much smaller that the loss of kinetic energy that I see for the truck.

10. May 3, 2016

### Staff: Mentor

Unfortunately no analogy will be perfect. You simply have to accept that the analogy is only vaguely like expansion and try to increase your knowledge of physics and math until you can learn the real theory.