Very simply it means that space and time when measured together are always continuous. Now the next question is what does Continuous mean here ? This is very complicated, so to answer this, we will start by discussing all the dimensions first.
0-Dimension- Can be considered as a small point which does not have any measurable length, width and height
1-Dimension- Is generally a line, that has only measurable length but no measurable width and height
2-Dimension- Is an object, where we can measure the length and width but not height
3-Dimension- Is an object, where we can measure all the 3, length, width and height
4-Dimension- Is that from where the complexity begins. It has length, width and height plus one more dimension which detects the changes in length, width and height. And it can be time/weight/volume depending on what and how we are measuring. Because the object matter changes itself with time. For example an ice-cube when taken out from a refrigerator is a cuboid, but as it melts it will become liquid water. So to measure the melted water, we will have to add one more dimension and we will call it volume.
Similarly you can take other examples where liquid gets converted to gas also on heating.
Now here instead of length, width, and height, we have added other dimensions also like volume or weight or time to do calculations on its size or behaviour.
5-Dimension- Here other than the 4 dimensions mentioned , the fifth dimension is added which is the rate at which all the above dimensions or measurements are being changed. It is the space-time ratio.
In the last blog, we showed that in all forms of matter(solids, liquids and gases), the space-time ratio is always changing. This constant change is the 4th-Dimension, and the 5th-Dimension is the rate at which space-time(4th-Dimension) is changing.
What is the significance of these dimensions ?
We will try to take real world examples for better explanation. And we will ignore the 0 and 1 dimension as they are rarely used.
2-Dimension, example letter
Let’s say you want to send a picture of size 8cm X 20cm to your friend in an envelope. As the photo only has a measurable length and width and no measurable height. Its evenelope can be of a size slightly bigger than the photo lets say 10cm X 22cm.
3-Dimension, example phone
Let’s say you have your mobile phone, and you want to pack it in a cuboid box for sending as a parcel. In order to perform this task, you will need to know the length, width and height of the phone. Lets say these values are (16cm X 8cm X 1cm). Now to create its packaging box, we will add 2 cm to the length, width and height of the phone. Now the dimensions for the packaging box are (18cm X 10cm X 2cm).
4-Dimension, example ice-cream on earth
If we were packing another solid object, let’s say ice-cream, then we know it may get converted from solid to liquid and vice-versa. So apart from length, width, height we will have to know the volume of the ice-cream as well, which will be lets say 200ml.
5-Dimension, example ice-cream in space
Now we will add more complexity to this. Let’s say we want to export this ice-cream to the nearest Asteroid. Refer to the picture above. We know that the space time ratio at our location inside the space-ship is 1:2.5 and at the asteroid it is 1:10
This means for every 1 second passed on the nearest planet/star 2.5 seconds pass in our space-ship and 10 seconds pass on the asteroid.
Every food item decays and has an expiration. So for simplicity we will assume that the ice-cream apart from getting melted also has an expiration of 100 seconds only. So we know that in 100 seconds it will not be good to eat and will have to be discarded. Life of ice cream is 100 s and constant at its location in space. But changes for other observers as per table below
| For an Observer at Point C near Asteriod | For an Observer at Middle Point B | For an Observer in Space ship at Point A | |
| space-time ratio relative to planet/star | 10 s | 5 s | 2.5 s |
| space-time ratio relative to Point A | 4 | 2 | 1 |
| Stationary icecream at 1-A | decays after 400 s | decays after 200 s | decays after 100 s |
| Stationary icecream at 1-B | decays in 200 s | decays in 100 s | decays in 50 s |
| Stationary icecream at 1-C | decays in 100 s | decays in 50 s | decays in 25 s |
| For an Observer at Point C near Asteriod | For an Observer at Middle Point B | For an Observer in Space ship at Point A | |
| Moving ice-cream 1-M first 40 s | partial decay in 160 s and 240 s remaining | partial decay in 80 s and 120 s remaining | partial decay in 40 s and 60 s remaining |
| Moving ice-cream 1-M second 60 s, after reaching Point B | decays in 120 s completely | decays in 60 s completely | decays in 30 s completely |
| Total decay time Observed (100 s) for ice-cream | 280 s | 140 s | 70 s |
There is fight between the customer at Point B and manufacturer Point A now:-
The customer at point B, will observe that normally the ice-cream 1-A took 200s when coming from Space Ship at Point A. So we have enough time, but due to space-time change the ice-cream expired mush faster than he expected, in just 140 s. The manufacturer at Point A checks again and finds that the ice-cream was moving in 5th dimension also so it expired in just 70 s, but if I had not sent it to Point B, it would have lasted 100 s. So the manufacturer, when packaging the ice-cream, apart from length, width, hieght, volume will have to specify the expiration value at the ‘source location space-time’ on the packing box of ice-cream as shown in picture.
You can see from the picture above that, all the 5 dimensions (length breadth, height, volume and expiration) details are mentioned as a single value on the side of the box. And the 5th dimension which is expiration is very important as it is changing every second, so the space-ship will change its speed to avoid ice-cream decay.
Also we can see that the space-time ratio which is continous, is written on the front of the box as a physical and unique address in Universe. This space-time co-ordinate label will tell the source and final destination of this package accurately. With this detailed information we have enough accuracy to make sure that both the customer and manufacturer are happy.
| We gain time when moving towards cog(center of galaxy) or heavy objects |
| We lose time when moving away from cog(center of galaxy) or heavy objects |
This example is to give you an idea about the complexities involved in transporting goods and moving from one location to another in deep-space. Also you can note that the above calculation is not accurate, because when we are moving from Point-A to the asteroid, the space-time ratio is also increasing from 2.5 to a higher value every moment. So the actual value of expiration time calculation will be even lesser than 140s or 70s.
I have given here only the example of ice-cream, but everything inside the space-ship(all machines and equipment) including your body will experience time differently. So just imagine the complexity involved in the calculation done by all the machines and the accuracy needed. This is why Astronauts have a very low-threshold for making errors and mistakes.
So if you are doing hard-work or working very fast. But your output does not match the desired result, your work is of no use. However, even if you are slow and not working very hard, your output matches the desired result. Then you are perfect!
How is space-time Continuous ?
Continuous means that it goes on and on and does not end as far as our ability and knowledge goes in measuring things and energy. It actually goes much beyond our abilities, but we stop as we cannot go further as it leads to more loss of our valuable time and efforts.
To prove that space-time is Continuous, we will do the opposite. We will assume that space-time is Discontinuous like all the other dimensions. And try to prove it false.
Again we ignore the 0 and 1 Dimension as it is not important for discussion here.
2-Dimension is Discontinuous ? Yes
Imagine drawing a square on a piece of paper which is 20 cm X 30 cm. Now let’s say if we have to draw or measure a square with length bigger than 30 cm, we cannot do it on this piece of paper. So what can we do? we can get a bigger paper, let’s say we get a bigger paper of length 1m x 1m. So far so good. What if we keep increasing the square width to 1 km or 1000 km. I think it is not possible. What we can do is break the square into smaller squares of lower lengths and then add them up.
The moment we agree upon breaking the bigger square into smaller square and then adding it up. We have made our measuring process “Discontinuous”.
3-Dimension is Discontinuous ? Yes
We will encounter the same problem in 3-Dimensions as well. As here instead of squares we build a cube of dimension 10 cm X 10 cm X 10 cm. And when we increase its size, we do not have long enough measuring tape. So, the above statement holds good.
4-Dimension is Discontinuous ? Yes
Volume, weight or time are also discontinuous. As we do not have very big weight or volume measuring devices. There is no consistency in time also across different time-zones of different countries.
5th-Dimension is Discontinuous ? No
There are 2 reasons:
1. It is the only dimension that measures the Discontinuity in 1,2,3,4 Dimensions. So it is continuous. Measurement in 5 dimensions can only be taken when a difference in reading comes in the 4 dimensions on any of the parameters measured. So it is also called a higher dimension. A higher dimension like 5th-dimension can look into lower dimensions easily. But a lower dimension cannot look into a higher dimension. So the job of a lower dimension is only to help the 5th dimension in accurate measurements.
2. A more complex and bigger explanation:-
We know that all matter has unique space-time ratios. And the process of calculating or measuring the space-time ratio of a distance of 1 kilometer in deep-space vacuum or 1 nanometer is same(it is Formulas).
Space-time ratios can give very accurate measurements like distances, time etc between planets, asteroids and stars which are millions or billions of kms. And it can also give very accurate measurements inside the atom’s nucleus as well.
We know that electric fields produce magnetic fields. And vice-versa. But if we get deeper into this statement, then actually there is no magnetic field as such in the universe. Refer the below picture, which is very similar to the ‘vicious circle’ image we had used in the previous blog.
When an electric field becomes almost discontinuous or almost loses its power, refer picture, then whatever field is remaining inside the leftover electric field, its effect on things around is opposite to that of the original electric field. So we name it differently with a new name “magnetic field”.
For a simpler explanation I will still use the word magnetic field to be more clear. We have the ability to measure electric fields and also magnetic fields.
Another example of continuity is the brightness of light that we observe everyday. Let’s assume that the light we receive on our house terrace is intense during the day because it comes from the closest star called the Sun. But in the night as the earth rotates to the opposite side, it becomes very less. Because at night the light is coming from very distant stars and not the Sun. However Brightness is not zero at any point in 24 hours. So we will assume the below:
Brightness of light during Day-> Electric Field
Dimness of light during Night(Darkness) -> Magnetic Field
We can make 2 statements regarding the same thing:-
1.) The light is bright during the day and decreases in the evening, and in the night it is completely dark. Then in the early morning darkness goes away and day is brightened again as we move from morning to afternoon.
2.) The light is very very bright during the day and decreases in the evening, and in the night it is very less bright. Then in the early morning brightness slowly increases and later it increases rapidly as we move from morning to afternoon.
So both above statements are saying the same thing. However, the first statement is easier to understand and explain. And the second statement does not have the word “dark” in it, so it is more complicated to understand as you have to count the number of times ‘very’ is used.
Similarly, we introduced magnetic fields everywhere in physics to make it simple. And as there is only one field in the universe called as the Electric field. All forms of energy, light energy, heat energy, mechanical energy, gravitational energy, electrical energy, sound energy, chemical energy, nuclear or atomic energy are only the manifestation of electric fields in varying degrees.
We have to name the same energy with different unique names, so that they could fit into our formulas for easier calculations.
No matter which place you go or imagine going in the Universe, we have only one force or field everywhere. And we have shown earlier that the electro-magentic field is just another name for the fundamental “electric field”. Also we know electro-magentic fields distort space-time.
Electric field ∝ Electro-magnetic Field ∝ Space-Time
So as the electric field is present everywhere, it is continuous. Similarly space-time will have to be continuous everywhere.
I do not want to write about any religion, but the electric field has very similar characteristics as the God has.
For example
– Omnipresent – It is present everywhere
– Omniscient – It does not know everything. But as it is present everywhere, we can know whatever we want to know by using and applying our knowledge.
– Omnipotent – It is definitely powerful, as it is the secret for all forms of energy we know.
We can go on and on, but I do not want to move away from the original discussion. But you can take it as an exercise, and find more such relations between God and the Electric field, and I am sure you will get the similarity.
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