Is Energy Conserved in Variable Time?
All real systems (macro and micro) experience time dilation.
Let’s recall mechanical definitions of energy and force units from school:
1 N — “Newton” is the force needed to accelerate 1 kg of mass at the rate of 1 meter/sec².
1 J — “Joule” is the work/energy done by 1-N force pushing a mass through a distance of 1 meter in the direction of the force applied.
In short, Joule is measured in kg×m²/sec², making dependency on sec (second) obvious, unless you believe in “Absolute Time”, like Newton did — that time flows at the same pace everywhere and always.
Other types of energy (chemical, electromagnetic, nuclear, etc.) are measured through some devices/processes, like a steam engine or Faraday’s apparatus/motor, converting one energy into another. Implicitly we rely on “energy conservation principle”, otherwise why would we be comparing energies of various types.
As Einstein discovered theoretically, and that was confirmed by measurements later, time passage is variable. Let’s denote by D time dilation in one area compared to another area: ratio of how much time in one area is slower than in another area. It is not a common knowledge that “time dilation” is directly connected to “absolute speed of light” c = 299,792,458 m/sec — all variability/locality is hidden in “sec” denominator:
Local to an area second is defined as a time span, during which a light ray travels a distance of 299,792,458 meters in this area.
Or to be more local: nanosecond is time for a light beam to travel 0.299 meters (about a foot).
Or in microworld: attosecond is time for a photon to travel 0.299 nanometers (about 3 angstroms).
All mechanical elements, starting from velocity (as distance per time, v = ΔS/Δt), strongly depend on time. Then what happens to an object crossing a timezone from a faster time area to a slower time area or vice versa?
Speed of the object increases when it comes to slower time and decreases when it comes to faster time. That already violates Newton’s 1st law of motion: “object remains in motion at constant speed unless acted on by a force”. (And there is more to it.) But that explains Mercury’s precession — first explained by Einstein:
Other laws become violated too, for example Newton’s 3rd law: Action = — Reaction. To save them, we need to account for time dilation D (classic laws stay for D=1 with no time passage difference). For example, for Newton’s 3rd law, the correct formula is: Action = — Reaction×D². Check explanation in Newton’s Third Law Is Violated: Action ≠ Reaction!
Now to the most interesting part: Is energy conservation really violated? We need to answer several related questions:
1. Does Joule (unit of energy) stay the same?
2. What happens to the energy formulas?
3. Do physical constants remain the same — are they constant in time passage (independent of pace of time flow)?
These questions are similar to the common questions like “Does $ (money unit) value change? Does your house value change?” Obviously, the buying power of the dollar changes. And the number of dollars increases in the system:
Obviously, inflation changes your grandpa’s house value. Better we should have asked: “Does the grandpa’s house value, inflation adjusted, stay the same or depreciate?”
And here is how energy-time relation works, all these are interconnected:
1. Joule in D-time slower time is D²-time greater than in the faster time.
2. Energy E = mc² of an object in D-time slower time becomes E = mc²D² in the faster time.
3. Instead of formula changing, it makes more sense to change constants: E = ℏ(D)×𝜈, where ℏ(D)=ℏ/D³ in D-time slower time. 14 billion years ago time was 2-time slower than it is now. 32 billion years ago, time was 12-time slower than it is now (without “Big Bang” cutoff). Thus, Planck’s constant was even smaller back then, and that lowers energy barriers for some processes to run in the past (similarly, inside atomic nucleus, where time is slower than our space time).
Details are in “Time Matters” free eBook (also available on Google and Amazon).
P.S. There is no space inflation/expansion — only time accelerates in the Universe. There are optical effects only: time dilation causes refraction by Snell’s law, convex or concave lensing. Check details in Why Einstein / Minkowski Space Bending Is Not Real?
