Time & Energy

Thought experiments on time, relativity, and the possible connection between time and energy

Thought Experiment: What is Time?

Time is one of the fundamental quantities in physics. In everyday life, it seems straightforward, but the theory of relativity shows that time does not pass equally for all observers.

In Everyday Life: We experience time as a sequence of events — past, present, and future.

In Physics: Time is measured by clocks. According to the theory of relativity, the measured time depends, among other things, on motion and gravity.

Time Dilation

Scientific Classification: The theory of relativity describes experimentally confirmed effects. The idea of a direct connection between energy and time dilation presented below, however, should be understood as a hypothesis or thought experiment.

Relativistic Time Dilation:

Δt = γ · Δτ γ = 1 / √(1 − v²/c²)

Here, Δτ denotes the proper time of the moving clock, and Δt denotes the corresponding time interval in another reference system.

Special Relativity Theory (SRT)

Time Dilation Due to Velocity

At high relative velocities, the time intervals of different observers differ. The effect is described by the Lorentz factor.

Δt = γ · Δτ γ = 1 / √(1 − v²/c²)

SRT Time Dilation Calculator

Calculate the Lorentz factor and relativistic time dilation.

50.0 % c
Observed time interval:
–
Lorentz factor: –

General Relativity Theory (GRT)

Time Dilation Due to Gravity

Clocks in different gravitational potentials can measure different proper times. In a weak gravitational field, this can be approximately described by:

dτ ≈ dt √(1 + 2φ/c²)

with the Newtonian gravitational potential

φ = −GM/r

GRT Time Dilation Calculator

The following calculator uses a weak-field approximation for the Earth's gravitational field.

Calculated proper time:
–
Difference: –

Note on Interpretation: The calculator describes a single clock in a simplified gravitational model. For real satellite clocks, among other things, motion, Earth's rotation, the exact geometry of the Earth, and additional relativistic corrections must be considered.

Own Theoretical Approach

Hypothesis: The following relationship is not part of the established theory of relativity. It is presented here as an own theoretical approach or thought experiment.

Δt' = Δt · f(Etotal / E0)

The function f would first need to be mathematically clearly defined. Subsequently, the hypothesis would need to provide testable predictions that can be compared with existing experimental results.

Development of Time Dilation Formulas

The following formulas are part of the special theory of relativity. The derivation can be intuitively understood using an idealized light clock.

1. The Light Clock

We consider two parallel mirrors with a distance L between them. A light signal travels from one mirror to the other and back.

Δτ = 2L / c

2. The Moving Light Clock

If the light clock is observed from a reference system in which it moves at velocity v, the light travels a longer path.

For half the distance, a right-angled triangle is formed. Half the mirror distance is L/2.

(cΔt / 2)² = (L / 2)² + (vΔt / 2)²

3. Solve for Δt

c²Δt² / 4 = L² / 4 + v²Δt² / 4 c²Δt² = L² + v²Δt² Δt²(c² − v²) = L²

From the proper time relationship Δτ = 2L/c, after appropriate transformation:

Δt = Δτ / √(1 − v²/c²)

4. The Lorentz Factor γ

The factor in front of the proper time is called the Lorentz factor γ:

γ = 1 / √(1 − v²/c²)

Thus, the time dilation formula is:

Δt = γ · Δτ

5. What Does γ Mean?

At low velocities, γ is very close to 1. As velocity increases, γ grows more and more. For velocities approaching the speed of light, the factor becomes very large.

Example: At v = 0.5c, we get approximately:

γ ≈ 1.1547

A proper time of 1 second corresponds to approximately 1.1547 seconds in the observed reference system.

6. Connection with Energy

For a particle with rest mass m₀:

E = γm₀c² E₀ = m₀c²

From this, it follows:

E / E₀ = γ

If we substitute this mathematical relationship into the time dilation equation, we get:

Δt = (E / E₀) · Δτ

Important Scientific Note:

This equation is a mathematical transformation of already known relativistic relationships. It does not prove that energy is the physical cause of time dilation.

Such a statement would be an additional hypothesis. It would need to provide an independent mathematical theory and testable predictions.

Experimental Confirmation of Relativistic Effects

Relativistic time differences have been experimentally investigated many times. Examples include measurements of muons, atomic clocks, and relativistic corrections in satellite navigation systems.

Examples of experimental tests of relativistic effects
Experiment / Application Effect Theory Time Period
Muons in the atmosphere Time dilation SRT 20th Century
Hafele-Keating Comparison of transported atomic clocks SRT + GRT 1971
GPS satellite systems Relativistic time corrections SRT + GRT Since the development of GPS

Differentiation: The experimental confirmation of relativistic time dilation does not automatically confirm an additional interpretation in which energy is the cause of this effect.

The Great Insight

The theory of relativity describes space and time as interconnected quantities. Motion and gravity influence the time intervals measured by clocks.

In addition, a mathematical connection arises from the relativistic energy formula between the Lorentz factor and the ratio of total energy to rest energy.

Comparison of established relativity theory with the own theoretical approach
Concept Relativity Theory Own Hypothesis
Space and Time Spacetime Interpretation via Energy
Energy Component of the relativistic description of physical systems Possibly fundamental role
Time Dilation Dependent on motion and gravity Energy dynamics as a hypothesis

My Conclusion

Energy is at the center of these considerations.

The reflection will be developed further, as there is still a lot of potential here.