Einstein famously stated, “Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore,” in response to Minkowski’s mathematical formulation of special relativity, particularly his concept of spacetime. These spacetime diagrams are still used to understand and  explain Relativity.

Just last year, I came up with interesting spacetime diagrams. I believe Einstein would have come up with similar diagrams if he had not accepted Minkowski’s spacetime diagrams.

There are four diagrams that add details incrementally and can be taught in schools and colleges.

BETTER WAYS TO VISUALIZE EINSTIEN’S RELATIVITY

1) Improvement over spacetime cones diagram :
Imagine you are a time traveler. You teleport between two spacetime regions with time running at different rates – 1 year at earth for every 1 second at planet X (a mysterious planet). When you trace your path as you teleport between the regions, you get Time Travel laws – You travel to future, You cannot travel to past, you always come to the present time.

Improvement compared to conventional spacetime cones: There is no movement in three dimensional space. There is no calculations involving speed of traveler or speed of light. In fact no speed of light limit and infinity. Infinity is inbuilt in this diagram.

Fig.1 proved spacetime diagram showing path of time traveler as he teleoprts between spacetime regions. Fig.2. Conventional SpaceTime Cone showing past and future light cone.

2) Improvement in two region spacetime diagrams:
This improves over the first diagram. We get parallel regions of space, one above the other, similar to time moving faster on earth under high gravity compared to space with low gravity. Time moves only in forward direction, as we naturally experience it. Here again you teleport between earth and planet X to reveal Time Travel laws.

Improvement compared to conventional two region spacetime diagrams: No calculations. We do not need to compare/calculate speeds of two travelers (which seems odd) to get their comparative rate of time passage (time dilation).

3) Improvements with multi-region space time diagrams: This time we have earth at the center with time running at normal rate of 1 second per second. We add regions with time moving faster below and regions with time moving slower above parallel to earth. with time running faster and faster as we go from top to bottom. We also now have time moving from past to future, with vertical axis at centre showing present time for all regions. All vertical lines are lines of simulteniety, showing events occurring at the same time for each region.
You are now free to hop to any region in this spacetime. You can’t travel to past, as you always hop using the vertical lines reaching the present time at any region.

Improvement over conventional multi-region space-time diagrams: It is possible to add multiple regions in conventional space-time diagrams from stationary observers perspective. But, it is impossible to see, plot and understand from each person’s perspective traveling at different speeds. Here we have only one person’s perspective, you, who hops, sees, understands time and imagines the world at each place. No calculations! We can use human understandable units for time – seconds, hours, days, years, million years. We have time dilation at 1/100 years at bottom and 100years at top, indicating time running at 100 years fast or slow for every 1 second on earth. There is no post calculations after calculating time dilation to understand the time elapsed at each place. No ultimate speed limit of speed of light! For the first time in history of relativity, we finally don’t have to deal with light. Where earlier space-time diagram stopped at infinity, these diagrams start with Infinity!

4) Improvements over curved space time diagrams: Rubber sheet curved space-time diagram? You now stretch the earlier diagrams proportionately to their rate of time passage (time dilaton). What you get is curved 2D time only (space-time) diagram. Now as you hop between the regions you clearly see yourself trace path to past and future, that was not obvious with in diagrams.

Improvement over conventional curved space-time diagram: 2D diagrams instead of 3D curved rubber sheet. Anyone can draw. You realise the curvature of space-time is due to curvature of time! Again for the first time in history of relativity, we make no distinction between special and general relativity! Heard about dimensions of space curved to a single point? Each point on the horizontal line for earth and other regions are 3D space curved to a single point! Any movement in 3D space has no effect on other regions, due the extreme difference in rate of time passage (time dilation).

LAWS OF TIME TRAVEL :

From the above spacetime diagrams we can summarize the laws of Time Travel as below:

• Time Travel to Future – Possible
• Time Travel to any time in Future – Possible
• Time Travel to Past – Possible
• Time Travel to any time in Past – Not Possible
• We always Travel to Present time.
• Time Traveler loses and gains time.
• Time runs at different rates.
• Lines of Simultaneity connects the present time of all the places.

These laws of Time Travel helps us imagine real challenges of interstellar space travel. What would happen if you teleport from a fast moving region to a relatively stationary region? Will you stand still or will you fall down? What would happen if you teleport from region of low gravity to high gravity? Can your body handle extreme gravity?

With these laws of Time Travel there is no place for paradoxes like grandfather paradox, where you freely travel to past and future.

MATHEMATICAL PROOF :

With no mathematical proofs how do we justify these new diagrams are correct? These diagrams come with there own formulas which are derived from existing Time Dilation formulas. But there is a slight difference. The time dilation is a factor, a ratio to speed of light, in existing formulas. The formulas below are in units of time in seconds.  We can orally do the calculations with simple time dilaton values like 2 seconds, 10 seconds and 100 seconds for the first formulas in two formula sets given below. The other formulas are just simple variations of the first formula, that go alongwith the diagrams.

1) Formulas for Speed of Traveller: Just check the first formula, you get the output as a ratio of traveler’s speed to speed of light. You multiply it with 100 and you get his speed (your speed, as you are hopping between spacetime regions) as percentage of speed of light.

Observe that at just 100 seconds the formulas give speed at almost 100% (99.995%) speed of light. The values become meaningless with higher time dilation values. But, the diagrams above works well with infinity in both directions – time running faster or slower than us.

2) Formulas for Gravity of the traveller: Here too, check the first formula. You can use the same values as above for time dilation 2 second, 10 second or 100 second. The constants c and G in the formulas are grouped together, leaving a single variable in the formula to work with. You get the output as a ratio of Mass (in Kilograms) to radius (in meters) of the planet you are hopping to. The formula looks very similar to above formulas. Now you can imagine any planet reducing and increasing Mass and radius to satisfy the ratio. You do not need the Mass and radius of actual planet. . These terms are separated and can be pre-calculated or kept as another constant.

You can read my preprint on the subject published in September 2024 here : https://zenodo.org/records/13625888
I held a webinar on the topic, which is available on YouTube : https://youtu.be/95PiqXbDbdA?si=gTROrPiUMTqmc0Cy

That is complete Relativity for you in one single post!

Disclaimer: These diagrams are well suited for introducing Relativity to kids and common people. They also help physicists visualise the cosmos without the burden of mathematical proofs. But that’s where the actual journey starts, and the rabbit hole goes deeper and deeper with every question you ask. You will then need to resort to conventional space-time diagrams, including the rubber sheet model.

Please let me know your thoughts in comments below. Can these diagrams be improved further? Can you add more laws to the list of Laws of Time Travel based on the diagrams? Please share and help debunk the misinformation around Time Travel.