How Can SPACE and TIME be part of the SAME THING?

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CHAPTERS
0:00 The most important concept in Physics?
2:00 Defining spacetime
3:15 The math of space vs math of spacetime
7:41 Let's answer your questions
8:41 How the heck can you add time and space in the formula?
10:12 The implications of combining space and time
11:10 Why not more than 3 spatial and 1 time dimension?
13:27 How to learn spacetime more deeply

SUMMARY
What is Spacetime? Are space and time the same thing? Space was thought to be nothing, an empty void with no matter in it. In 1908, Hermann Minkowski postulated that time could be thought of as a 4th dimension along with the three dimensions of space. Einstein later showed that this spacetime is a kind of geometry that can bend, affecting the trajectory and passage of time for objects. How can space and time be part of the same canvas? Space is measured in meters, while time is measured in seconds. How are the two interchangeable?

The definition of spacetime is the set of points in space and time, located with 4 numbers. This would be the location in 3 dimensional space and a time. You can also call these events.

In ordinary Euclidean space, the distance between two point A and B is fairly simple to figure out. The straight line between them is the shortest path. And it’s obvious also that any other path, from A to B will be longer.

If we change one of the coordinates to time, the math that we need is not based on Euclidean geometry, but Minkowskian geometry (or Minkowski Geometry). The straight line between A and B does not represent distance but time elapsed between two events. A straight line represents traveling at a constant velocity between the two events, and is the MAXIMUM duration. So for example, in spacetime, if you took a curved path from event A to event B, or a zig zag path, then the elapsed time would be lower compared to the straight line between A and B, because you will have traveled more in space than in time.

Einstein showed that there is no such thing as absolute time, and so that’s why we have a new formulation. But how do you add time and distance together, since the units are completely different? The key is that there in important conversion factor between time and space, that allows us to convert one to the other. And that conversion factor is, the maximum speed limit of the universe, that is, as far as we know, is the speed of light. The speed of light is the key to uniting space and time. We call this maximum speed “c” in physics.

And c is 299,792,458 meters per second. As you know speed is distance over time. If we multiply this speed by time, we get a distance. So now we can convert time in the same equation to distance – distance = c*t. Thus, the equation works by using this conversion factor.

This formulation for a 2 dimensional spacetime can be extended to the real 4 dimensional spacetime we live in. And that 4 dimensional geometry is the foundation for understanding General Relativity, with the addition that this spacetime is no longer flat, but can curve and contort. So the math gets complicated in General Relativity. The consequence of a curving spacetime is that this results in gravity.

Why do we have only 3 dimensions, why not more? And why not more than one time dimension? First, large spatial dimensions probably don’t exist because we would have detected them if they did. And more than one dimension of time could result in closed time-like loops, in other words it would allow travel to the past. This is considered an impossibility because it would break causality.

More than 3 spatial dimensions would also likely have fatal consequences. In 1920 Paul Ehrenfest showed that our orbit around the sun would be impossible if we had an additional spatial dimension. Other problems have also been identified, for example the orbit of the electron in atoms would become unstable.
#spacetime
If we had fewer spatial dimensions, then spacetime would be too simple for life. For example if we had only one spatial dimension, then orbits could not form. Two dimension would also probably be too simple to result in life.

[meghjoshi]

Space and time are relative, the more time I spend with my relatives the more space I need

[wayneyadams]

My favorite concept which I read way back when I was in Junior High school is that "when you travel at any speed you trade space for time." You gain time (time dilation) and you lose space (length contraction).

[binhta]

Wow, I just happened to come across this video and I found the explaination super helpful with such a complex concept (you can tell that I'm not a science major here). The use of interactive graphics really helps guide the viewers to have a better understanding of the talk. But the real genius is how Mr. Arnold breaks the concept down and use simple languages to clarify the complexities of space-time (I'm still not there yet but may be I will someday). STEM students can truly benefit from this type of education. I'll definitely keep following this and hope my granddaughter will benefit from this someday, should she chooses to go into science/engineering. Thank you.

[life_score]

That’s a lot of difficult key concepts packed into one easier to understand video, bravo! 👏

[comatronic]

No one can make me understand, or believe to understand, complex physics like Arvin.

[shethtejas]

Hello Arvin. You should be made the education minister for the whole world owing to your exceptional pedagogic skills. Schools in general tend to repress creative questions from children. Someone like you would reverse that and then we will not just be finding new answers, but we will also be finding new questions, both of which are paramount for scientific progress.
Excellent video as always. I especially liked you putting a very obvious question 'how can two quantities with different dimensions be equated'. One question: In the video you mentioned that multi dimensional time would allow time loops to exist. How is it then that we humans are trying to invent a time machine in a space-time which has only one dimension for time? Shouldn't it be outrageously impossible?

[Yewbzee]

The bigger question revolves around whether spacetime, the foundation of our current physics models, can still be considered the fundamental layer of reality, or if it instead originates from a more foundational underlying structure. While our current models have thrived on the spacetime framework, recent challenges and breakdowns in certain areas have prompted us to question whether spacetime alone can continue to provide a comprehensive explanation.

[datachief]

This is EXCELLENT! I have tried to come to terms with spacetime for ages, but Arvin has shed light where no-one else has been able to. Thank you!

[hahahasan]

I love that you casually gave one of the most intuitive explanations for the twin paradox as an aside for your main subject matter. Your talent and hard work as an educator is so incredibly rare. Thank you.

[philjamieson]

I love your commentary; it's so concise and ultra clear. Those two things really help me to grasp these complex ideas.

[dougg]

Time adjusts itself for each person to make sure light speed is the same for each person/observer ( whatever that is). Crazy

[aanchaallllllll]

0:08: 🌌 The concept of space-time is essential for the existence of the universe and all physical phenomena.
2:54: 🌐 The concept of combining space and time into a 4-dimensional continuum called spacetime is not intuitive, but can be understood by comparing it to the geometry of space.
5:31: ⏳ Time and space have an inverse relationship, as shown by the equation E^2 = t^2 - x^2.
8:21: ⏳ The concept of time and its relationship with space explained, including the conversion between the two using the speed of light.
11:09: 🌌 The existence of 3 spatial dimensions and 1 temporal dimension is crucial for the existence of life and to avoid paradoxes.
13:53: 📚 Brilliant offers a practical course on Special Relativity with interactive learning tools and monthly new content.
Recap by Tammy AI

[tariqmalik]

One of the simplest best presentation of space time. For our future young generation scientist, it is very important to understand the space time concept. It is necessary to extend our understnding of Einstein's Theory of relativity, his EMC² and also the new concepts on Gravitation...is not a force and beyond. As usual, good job from ARVIN.

[rva]

This is such an amazing encapsulation of a difficult topic. I could have skipped dozens of videos by simply starting here!

[vijaysahani]

Dear Arvin sir, you have simplified complex topic to a great extent. Love you.

[ericwilson]

Great video! I find it helpful to think speed is converted from time. We are all moving through time at the speed of light. You hinted at the conversion factor… borrowing just a little time and can give you a lot of extra speed

Gravity is constant acceleration so we need speed to overcome that and appear stationary. So we convert some of our time to speed so our time goes a little slower.

[RGF]

The explanations in this video as to why there are exactly 3 spatial dimensions and one time dimension in space/time seems to provide an argument against string theory, which requires either 11 or 26 spatial dimensions depending on symmetry considerations.

[ridethecurve]

Back in ancient Greece, the big things were Earth, Air, Fire, Water. To me, these should be changed to Space, Time, Matter and Energy, with the first two and second two interchangeable with one another. It's a really interesting topic to me, so I'll be back to watch more of these videos, for sure! Thanks.

[chrislocke]

Arvin, this was a wonderful presentation, made beautiful because of your faith. Your love of creation really came out and really makes this video special (not relatively, absolutely).
After 23 seconds “space time, the canvas, that the Painter with all the colours needed to create their master piece”
And at the end, the fine tuning,
If the universe were any different, one dimension more one less, and we wouldn’t exist
Finally, you gave thanks along with the loving couple gazing at the stars.
You mentioned thanking your lucky stars- but I take this as code word for thanking something else that really does exist. God bless you.

[dactylntrochee]

On one hand, this is the closest I've ever come to grasping the concept, so bravo for Arvin. On the other hand, if C is distance/time, then C squared would be distance squared over time squared. Well, I know what a distance squared is (three inches on the sides of a square yields nine square inches), but I can't grasp the meaning of a time squared. What's a square second? This continues to flummox me.

Still, it's the clearest demonstration of the concept I've seen so far, and my livelihood doesn't depend on my understanding it, so I'm satisfied for today.