Thought Experiments

Time & Energy

Thought Experiment: What Is Time?

Time is one of the fundamental quantities in physics. In everyday life, it seems self-evident, but the theory of relativity shows that time does not pass at the same rate for all observers.

In everyday life: We experience time as a sequence of events – the past, the present and the future.

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

Time Dilation

Scientific classification: Relativity describes experimentally confirmed effects. The idea presented below of a direct link between energy and time dilation, on the other hand, should be understood as a hypothesis or thought experiment .

Relativistic time dilation:

Δt = γ · Δτ γ = 1 / √(1 − v²/c²)

Here, Δτ is the proper time of the clock moving with the body, and Δt is the corresponding time interval in another reference frame.

Special Theory of Relativity (SR)

Time Dilation Due to Velocity

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

Δt = γ · Δτ γ = 1 / √(1 − v²/c²)

SR Time Dilation Calculator

Calculate the Lorentz factor and the relativistic time dilation.

50,0 % c
Observed time interval:
–
Lorentz factor: –

General Theory of Relativity (GR)

Time Dilation Due to Gravity

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

dτ ≈ dt √(1 + 2φ/c²)

with the Newtonian gravitational potential

φ = −GM/r

GR Time Dilation Calculator

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

Calculated proper time:
–
Difference: –

Interpretation note: The calculator describes a single clock in a simplified Gravity model. For real satellite clocks, factors such as motion, the Earth’s rotation, the exact geometry of the Earth and further relativistic corrections must be taken into account.

Own Theoretical Approach

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

Δt' = Δt · f(Eges / E0)

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

Development of the Formulas for Time Dilation

The following equations relate to special relativity. The derivation can be clearly understood using an idealised light clock as an example.

1. The Light Clock

Consider two parallel mirrors separated by a distance of L. A light signal travels from one mirror to the other and back again.

Δτ = 2L / c

Δτ bezeichnet hier die Proper time, also die von der mitbewegten Lichtuhr gemessene Time.

2. The Moving Light Clock

If one observes the light clock from a reference frame, in which it moves with velocity v the light travels along a longer path.

A right-angled triangle is formed halfway along the path. Half the mirror distance is L/2.

(cΔt / 2)² = (L / 2)² + (vΔt / 2)²

3. Solving for Δt

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

Using the proper-time relation Δτ = 2L/c follows after appropriate processing:

Δt = Δτ / √(1 − v²/c²)

4. The Lorentz Factor γ

The factor multiplying the proper time is called the Lorentz factor γ and is defined as:

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 the velocity increases, γ grows ever faster. For velocities approaching the speed of light, the factor becomes very large.

Example: At v = 0,5c the result is approximately:

γ ≈ 1,1547

A proper time of 1 second therefore corresponds to approximately 1.1547 seconds in the reference frame under consideration. 1.1547 seconds.

6. Relationship with Energy

For a particle with rest mass m₀:

E = γm₀c² E₀ = m₀c²

This gives:

E / E₀ = γ

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

Δt = (E / E₀) · Δτ

Important Scientific Note:

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

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

Experimental Confirmation of Relativistic Effects

Relativistic time differences have been studied experimentally on numerous occasions. Examples include measurements of muons, atomic clocks and the relativistic corrections used in satellite navigation systems.

Examples of experimental tests of relativistic effects
Experiment / Application Effect Theory Date
Muons in the atmosphere Time Dilation SRT 20th century
Hafele-Keating Comparison of transported atomic clocks SRT + ART 1971
GPS-Satellitensysteme Relativistische Timekorrekturen SRT + ART since the development of GPS

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

The Big Insight

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

Furthermore, the relativistic energy formula establishes a mathematical relationship between the Lorentz factor and the ratio of total energy to rest energy.

Comparison of established relativity theory with our own theoretical approach
Concept Relativity Own Hypothesis
Space and Time Spacetime Interpretation in terms of energy
Energy An integral part of the relativistic description of physical systems Possibly a fundamental role
Time Dilation Dependent on motion and gravity Energy dynamics as a hypothesis

My Conclusion

Energy is at the center of these considerations.

These ideas will be developed further, as there is still considerable potential here.