(Originally posted on Monday, 12 October 2026)
Most newcomers in cue sports (typically in American 8-ball pool) have NO IDEA about some very useful simple things that can help them immensely. It seems to me that some cue sports coaches HIDE some information from their students in order to earn more money by giving more “lessons” to struggling newcomers/amateurs.
Fortunately we live in wonderful times of Youtube and we can learn some crucial things on our own. Ironically, now the problem is that there are TOO MANY useful videos to watch, so I prepared a concise summary of the BEST tips for newcomers in cue sports (typically in American 8-ball pool) that were very useful to me.
I will give the tips in an order that shows that many useful things may be learned IN ADVANCE, even before attempting a single shot.
1. Realize that with a half-ball hit the potting angle is ONLY 30 degrees.
All the other things, including your technique, your bridge, your stance and your cueing action, are useless if you visualize/calculate angles in an incorrect way. I believe many amateurs keep missing some shots ONLY because they visualize relatively big potting angles in a clearly WRONG way. I had been doing it myself.
A half-ball hit is when the middle of the white/cue ball is aimed at the edge of an object ball. When I was younger I had thought that in such case the angle was 45 degrees, so when I learned that it's actually ONLY 30 degrees I was SHOCKED! Here's my own (recent) visualization of the two angles (the second picture is a close-up):
Just look how much OUTSIDE of the object ball you have to aim in order to achieve the angle of 45 degrees!
If you want very good visualizations of different angles just watch this video from 1:26 to 7:14 (times already set):
The problem is that in reality it's very hard to “calculate” angles other then half-ball hit, so the main thing I do is to decide if the angle is bigger or smaller than 30 degrees, so I know if I have to aim outside or within the object ball. With angles clearly smaller than 30 degrees the ghost ball can be very helpful, but with bigger angles the usefulness of the ghost ball is very limited, so it's all about experience.
2. Keep the cue as level as possible.
When I finally learned about the importance of keeping the cue as level as possible my potting on relatively long shots improved INSTANTLY!
If the cue is NOT level then any side-spin, even a tiny one, introduces SWERVE, which means that the path of the white/cue ball is in some part CURVED. Just watch this video from 0:56 to 1:56 (times already set):
3. Be aware of the existence of the cut-induced throw.
The cut-induced throw is connected with a relatively small friction force that acts at the contact point along a different line than the main force, so the effective force is slightly different. On short and/or strong shots it doesn't matter, but on long and relatively weak shots it may cause a missed shot. Open in a new tab to enlarge:
4. Avoid using any side-spin.
This tip is connected with the point 3 BUT there are MORE disadvantages of a side-spin than just swerve! Let's separate them.
4.1. Avoid using any side-spin to avoid SWERVE.
It's practically impossible to keep the cue perfectly level, which means that ANY side-spin is connected with a SWERVE (like it was described in the previous point). What's worse, swerve depends also on shot strength/speed, which introduces another level of complexity. Just watch this video from 10:54 to 12:59 (times already set):
4.2. Avoid using any side-spin to avoid SQUIRT / DEFLECTION:
EVEN if the cue is perfectly LEVEL, a side-spin still makes the white/cue ball move in a slightly different line than the aim line – this effect is called squirt/deflection. Just watch this video from 7:02 to 8:07 (times already set):
When the cue is perfectly level different side-spins require different corrections for squirt/deflection. Just watch this video from 0:37 to 1:31 (times already set):
The amount of time needed to obtain enough experience to be able to correctly apply the correction for squirt/deflection for various side-spins must be HUGE! It's clearly beyond the possible abilities of typical amateurs (with significantly limited playing/practicing time).
4.3. Avoid using any side-spin to avoid a CHANGE in potting angle due to the spin-induced throw.
EVEN if you correctly apply the correction for squirt/deflection, a side-spin ON ITS OWN changes a potting angle due to the spin-induced throw (the spin throws the object ball from the “correct” potting angle).
It's easiest to understand with a straight shot – here's an image of forces acting on the object ball:
So, a side-spin introduces another, relatively small friction force acting at the contact point along a different line, so the effective force is slightly different. On short and/or strong shots it doesn't matter, but on long and relatively weak shots it may cause a missed shot, just like the cut-induced throw (described in the point 3).
The spin-induced throw can act one of TWO ways, unlike the cut-induced throw. The spin-induced throw for an INSIDE side-spin ADDS to the effect of the cut-induced throw, while the spin-induced throw for an OUTSIDE side-spin CORRECTS (more or less) the effect of the cut-induced throw.
In some cases the OUTSIDE side-spin may help to achieve a perfect potting angle by perfectly compensating the cut-induced throw, like this (open in a new tab to enlarge):
The problem is that it's very hard to correctly apply the amount of side-spin AND at the same time to correctly apply the correction for squirt/deflection (see the previous sub-point).
4.4. Summary of the sub-points 4.1., 4.2. and 4.3.
A side-spin with an elevated cue (even only slightly elevated) causes THREE different things AT ONCE (squirt/deflection, swerve and spin-induced throw), so it's EXTREMELY hard to predict the COMBINED effect.
Players who practice DAILY for HOURS have a very good feel for such shots, but a newcomer should AVOID using any side-spin almost completely (see the point 10 for a LONE exception).
A newcomer should learn how potting angles “work” without using any side-spin. Otherwise (when learning while using a side-spin) a newcomer is likely to miss some shots that otherwise (without a side-spin) would actually be successful. Too much confusion for a newcomer!
5. Understand that a top-spin = white/cue ball ROLLING on a table.
This is crucial for understanding why the top-spin is so easy to obtain. When I (finally) realized this connection (top-spin = white/cue ball ROLLING on a table) I recorded a video that is the ultimate proof (obtaining top-spin while pushing the white/cue ball at its bottom part) AND that shows that the effect is stronger when the white/cue ball is rolling faster (as simple as that):
For a better top-spin we have to aim higher at the cue ball just to make the cue ball START to ROLL as quickly as possible (instead of slide on a table without any spin, or even with a back-spin, for some time) – this way we conserve as much energy of our hit as possible for the proper ROLLING movement. With a stun shot, and even more so with a back-spin, lots of energy is wasted by the friction of the cue ball sliding on a table. On the other hand ROLLING friction is much smaller, so less energy is wasted.
6. Forget about back-spin on medium and long shots.
A back-spin on medium and long shots is EXTREMELY hard to obtain, so a newcomer shouldn't even try do to it. With a back-spin lots of energy is wasted by the friction of the cue ball sliding on a table and this is why the back-spin sooner or later wears off and naturally transforms into a rolling movement, so into a top-spin.
When the white/cue ball is close to the object ball it's easier to apply back-spin, BUT I myself miss more shots then (when comparing to non-back-spin shots). I sometimes use it, but only when I'm desperate.
7. Try to develop a steady bridge.
Just watch this video from 4:04 to 9:26 (times already set):
8. Try to develop a repeatable stance.
Just watch this video from 3:43 to 5:45 (times already set):
9. Put your chin on the cue.
A repeatable cue action is probably the hardest thing to achieve by an amateur. For example I myself from time to time mess up a shot in such a way that the white/cue ball travels significantly to the left side from the line I wanted it to go along. It's most pronounced on long shots, but it must be happening (from time to time) on all types of shots. On some bad days, when I struggle with it on too many shots, I try to consciously “correct” my aim to the right and I end up messing up the next shot. Honestly, this is so frustrating that I simply accepted the fact that I mess up some shots from time to time, mostly because I don't have time nor will to practice this aspect of my game.
HOWEVER there is one thing that is actually useful and improves things a little – putting your chin on the cue. It helps to physically feel if the cue is moving in a straight line. The problem is that your stance has to be low enough, so the cue is almost level (at the table's height).
Here's a video referring to older people, who are not as agile as young ones, that points out the importance of putting your chin on the cue, even at the cost of using a non-typical stance – just watch from 1:27 to 2:40 (times already set):
10. It's SAFE to use an OUTSIDE side-spin on SHORT shots with BIG CUTS.
This is a LONE exception to the point 4. (“Avoid using any side-spin”) and I myself use this shot regularly.
With an OUTSIDE side-spin THREE things happen simultaneously:
1) there is squirt/deflection that makes the white/cue ball travel along a different line, so the potting angle becomes a little off, but with a short shot the effect is very small,
2) the cut-induced throw makes the potting angle even more off, as usual,
3) with significant outside side-spin the spin-induced throw is STRONGER than the cut-induced throw, which compensates for BOTH effects from the points 2 and 3.
Open in a new tab to enlarge:
The combined effect is still to the same side as the cut-induced throw, but it's BETTER than when trying to pot the object ball without any side-spin, because the object ball is hit more thick (less risk of missing it completely) but it still goes in. Here's my example:
Why a little top-spin? It stabilizes the movement of the white/cue ball by minimizing the sliding phase at the start, which by the way conserves the energy of the shot. Just watch this video from 12:53 to 14:06 (times already set):
An OUTSIDE side-spin (with a little top-spin) on SHORT shots with BIG CUTS in some cases allows spectacular positioning, like this:
The sheer energy of the white/cue ball moving around the table is a joy to watch! In such positioning an OUTSIDE spin ADDS speed to the white/cue ball at FOUR different places – first at the object ball (very small addition, but still) and then at THREE cushions! In this case the spin was still quite strong when the white/cue ball hit the fourth cushion, but it happened on the “wrong side of the side-spin” and this is why the white/cue ball slowed down significantly.
Overall my shot was actually too strong (far from perfect position to pot the black ball), but it means that a similar positioning, for example on just three cushions, is within reach of a newcomer.
11. Do NOT try to imitate professionals, even on breaks.
According to the WPA rules for 8-ball, if no object-ball is pocketed, at least four object-balls must be driven to one or more rails. Newcomers often struggle with achieving a legal break, but there is a position that practically guarantees a legal break even with a relatively weak shot. When you place the white/cue ball behind the Head String at the place corresponding to the end of the object ball triangle and aim straight to the top ball of the triangle then at least four balls are driven towards cushions with relatively big energy, like this:
Which exactly cushions are hit is a little random because even a tiny difference in triangle placement OR a tiny difference in shot aim is enough to alter all the ball movements significantly. In this case I didn't hit the top ball of the triangle perfectly straight and this is why the white/cue ball went a little to the left.
With such a break it's actually possible to pot even two balls, like this (but it's very rare – I did it only once):
Did you notice how the white/cue ball stopped completely still, giving away all of its energy? Unfortunately it's very hard to hit the top ball of the triangle perfectly straight, which means that usually some energy of the shot is wasted. For really good players it doesn't matter because their break shot is extremely strong, but for a newcomer every little thing is important. Not to mention that really good players use a special break cue, which allows extremely strong break shot that would break the standard cue (a pun intended).
On a side note: I LOVE weak amateur 8-ball breaks because the object balls remain quite clustered, so even very good players have trouble to clear the table in one attempt. This is why I NEVER hit with full power (not even close), although I usually try to obtain a semi-weak break, so I hit relatively strong (rather than consciously weak).
By the way, I HATE when some people think/suggest that all the amateur players should try to imitate professionals, especially while breaking. It's PATHETIC to encourage your opponent to play to YOUR strengths.
12. Aim straight at the top ball in the triangle.
Yes, I repeat what I already wrote, but it's crucial for newcomers. In the break below LOTS of energy was retained in the white/cue ball (it moved first to the right cushion and then all the way to the left cushion) just because my son hit the top ball far from straight.
By the way, it's a kind of record for the weakest legal break in American 8-ball pool. ONLY 4 balls separated significantly from the triangle and they all touched at least one cushion. The last of the 4 balls did it just barely and we started laughing. It was crucial (for achieving the “record”) how much energy was transferred (through other balls) to the 13 ball – it went around the table, hitting all 4 cushions and ended up not far from the center. So, most of the shot energy was contained in just two balls (the white/cue ball and the 13 ball) and the rest of the energy was transferred mostly to the other 3 balls that reached the cushions. The rest of the balls barely moved. What a shot! Sort of.
Summing up:
Learning from your own mistakes will take forever if you don't even know that you keep committing a particular mistake, especially if you visualize/calculate angles in an incorrect way.
Monday, 12 October 2026
Thursday, 3 September 2026
Eurosport focusing on tennis is fucking pathetic!
(Originally posted on Thursday, 3 September 2026)
Eurosport focusing on tennis (precisely on the US Open) is fucking pathetic! All the people from Eurosport who think that everybody likes tennis are complete morons. I hate tennis and on BOTH Eurosport channels there is mostly tennis right now. Hour, after hour, after hour. Revolting!
What's worse there is absolutely no snooker, even thought there is the British Open right now. Pathetic! Fucking pathetic! By the way, snooker is losing fans this way.
And don't even start with me that I should use a paid channel/platform – I will never pay significant money for any channel/platform because to cover everything I would have to pay huge total money for SEVERAL channels/platforms! No fucking way. “This world will not impose its will. I will not give up and I will not give in!” “And I won't duck and run cause I'm not build that way.”
I don't believe the absolutes anymore
I'm quite prepared to admit I was wrong
This life, it sucks your principles away
You have to fight against it every single day
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
It is like so many other things
As distant as your former sins
So sad and lonely and so derelict
As the optimism that we once shared
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
I'll send you postcards every single day
Just to prove I still exist
This world will not impose its will
I will not give up and I will not give in
And I will not give up and I will not give in
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
I won't betray your confidence
I won't pretend my way was lost
This world will not impose its will
I will not give up and I will not give in
This world will not impose its will
I will not give up and I will not give in
Eurosport focusing on tennis (precisely on the US Open) is fucking pathetic! All the people from Eurosport who think that everybody likes tennis are complete morons. I hate tennis and on BOTH Eurosport channels there is mostly tennis right now. Hour, after hour, after hour. Revolting!
What's worse there is absolutely no snooker, even thought there is the British Open right now. Pathetic! Fucking pathetic! By the way, snooker is losing fans this way.
And don't even start with me that I should use a paid channel/platform – I will never pay significant money for any channel/platform because to cover everything I would have to pay huge total money for SEVERAL channels/platforms! No fucking way. “This world will not impose its will. I will not give up and I will not give in!” “And I won't duck and run cause I'm not build that way.”
I don't believe the absolutes anymore
I'm quite prepared to admit I was wrong
This life, it sucks your principles away
You have to fight against it every single day
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
It is like so many other things
As distant as your former sins
So sad and lonely and so derelict
As the optimism that we once shared
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
I'll send you postcards every single day
Just to prove I still exist
This world will not impose its will
I will not give up and I will not give in
And I will not give up and I will not give in
These are the postcards from a young man
They may never be written or posted again
These are the postcards from a young man
They may never be written or posted again
I won't betray your confidence
I won't pretend my way was lost
This world will not impose its will
I will not give up and I will not give in
This world will not impose its will
I will not give up and I will not give in
Tuesday, 1 September 2026
We are all brain-dead motherfuckers
(Originally posted on Tuesday, 21 November 2017)
Nobody is perfect and everybody has his (or her) own “demons”. To me it has always been my addiction to computer games and to lesser extent my addiction to chess. I have been kind of lucky because there are much more dangerous addictions than mine (like alcohol or narcotics), but there are also other things that make us all morons anyway.
The problem is that at some moments we consciously ignore our own common sense (a kind of “voice inside our head”) when it tells us that we should not do what we are about to do. I'm talking not only about addictions that are repetitive, but also about some single events that can end up very bad for us. We also ignore some “suggestions” to do something good for us, even when we know perfectly well that the “suggestion” is correct.
Below there is the song Miss Europa Disco Dancer by Manic Street Preachers that features some lyrics that are utterly universal and thought-provoking. More importantly the final phrase of the song, repeated 23 times, gives a surprisingly positive feeling. Well, I must admit that the first time I have heard this song I was irritated by such an ending, but over time I appreciate it more and more. By the way: only Manics can combine harp with such lyrics!
Miss Europa disco dancer
Feel the drug of your persona
Miss Europa disco dancer
I'm in heaven when I see ya
Miss Europa disco dancer
Favourite son and favourite daughter
Miss Europa disco dancer
Suck - suck up all of your power
So serene the world turns blue
Heads are spinning – it feels so good
It's poetry, sheer poetry
The way you destroy your beauty
Miss Europa disco dancer
Brutally becomes a no hoper
Miss Europa disco dancer
Had your luck and had your chances
Miss Europa disco dancer
Never reached the super-nova
Miss Europa disco dancer
Wake up drunk and then fall over
So messed up the world turns grey
All washed up with debts to pay
It's agony, sheer agony
The way your life just fades away
So serene the world turns blue
Heads are spinning – it feels so good
It's poetry, sheer poetry
The way you destroy your beauty
So messed up the world turns grey
All washed up with debts to pay
It's agony, sheer agony
The way your life just fades away
Brain-dead motherfuckers (x23)
Nobody is perfect and everybody has his (or her) own “demons”. To me it has always been my addiction to computer games and to lesser extent my addiction to chess. I have been kind of lucky because there are much more dangerous addictions than mine (like alcohol or narcotics), but there are also other things that make us all morons anyway.
The problem is that at some moments we consciously ignore our own common sense (a kind of “voice inside our head”) when it tells us that we should not do what we are about to do. I'm talking not only about addictions that are repetitive, but also about some single events that can end up very bad for us. We also ignore some “suggestions” to do something good for us, even when we know perfectly well that the “suggestion” is correct.
Below there is the song Miss Europa Disco Dancer by Manic Street Preachers that features some lyrics that are utterly universal and thought-provoking. More importantly the final phrase of the song, repeated 23 times, gives a surprisingly positive feeling. Well, I must admit that the first time I have heard this song I was irritated by such an ending, but over time I appreciate it more and more. By the way: only Manics can combine harp with such lyrics!
Miss Europa disco dancer
Feel the drug of your persona
Miss Europa disco dancer
I'm in heaven when I see ya
Miss Europa disco dancer
Favourite son and favourite daughter
Miss Europa disco dancer
Suck - suck up all of your power
So serene the world turns blue
Heads are spinning – it feels so good
It's poetry, sheer poetry
The way you destroy your beauty
Miss Europa disco dancer
Brutally becomes a no hoper
Miss Europa disco dancer
Had your luck and had your chances
Miss Europa disco dancer
Never reached the super-nova
Miss Europa disco dancer
Wake up drunk and then fall over
So messed up the world turns grey
All washed up with debts to pay
It's agony, sheer agony
The way your life just fades away
So serene the world turns blue
Heads are spinning – it feels so good
It's poetry, sheer poetry
The way you destroy your beauty
So messed up the world turns grey
All washed up with debts to pay
It's agony, sheer agony
The way your life just fades away
Brain-dead motherfuckers (x23)
Friday, 7 August 2026
Milly Alcock AND the DC Studios will NEVER get a single penny from me!
(Originally posted on Thursday, 2 July 2026; updated on 7 August 2026)
This pissed me off:
“And it’s from a lot of people whose profiles have no photo, who are burner accounts. Or someone’s name and then ‘Dad of four, Christian,’ which is hilarious to me. But I mean, whose opinion do you really care about? If you’re pissing the right kind of people off, you’re doing OK”
Milly Alcock said it as if being a father of four was something wrong AND as if being a Christian was something wrong. I myself am a father of three, but we (me and my wife) agreed that if we moved back in time we would have four children. We are Christians too, but there is nothing wrong with that. On the contrary – Christians respect everybody WITHOUT allowing harm on other people, so for example we will always be AGAINST destroying young generation on purpose (against something that is being actively done by some leftist madmen).
There is no fucking way Milly Alcock will get a single penny from me and there is no fucking way the DC Studios will get a single penny from me. EVER. The DC Studios didn't comment on that interview by Milly Alcock, which means that they see nothing wrong with what she said. No fucking penny for you! EVER.
UPDATE:
Some of the “defenders” of Milly Alcock are really stupid – I found a hilarious response to some illogical shit they write:
Ha, ha, ha !!!
This pissed me off:
“And it’s from a lot of people whose profiles have no photo, who are burner accounts. Or someone’s name and then ‘Dad of four, Christian,’ which is hilarious to me. But I mean, whose opinion do you really care about? If you’re pissing the right kind of people off, you’re doing OK”
Milly Alcock said it as if being a father of four was something wrong AND as if being a Christian was something wrong. I myself am a father of three, but we (me and my wife) agreed that if we moved back in time we would have four children. We are Christians too, but there is nothing wrong with that. On the contrary – Christians respect everybody WITHOUT allowing harm on other people, so for example we will always be AGAINST destroying young generation on purpose (against something that is being actively done by some leftist madmen).
There is no fucking way Milly Alcock will get a single penny from me and there is no fucking way the DC Studios will get a single penny from me. EVER. The DC Studios didn't comment on that interview by Milly Alcock, which means that they see nothing wrong with what she said. No fucking penny for you! EVER.
UPDATE:
Some of the “defenders” of Milly Alcock are really stupid – I found a hilarious response to some illogical shit they write:
Ha, ha, ha !!!
Sunday, 14 June 2026
Gravity – an elliptical orbit marks a perfectly round donut!
(Originally posted on Sunday, 14 June 2026)
Recently I was toying with an old Flash game titled The Orbit Game and I discovered that an elliptical orbit marks a perfectly round donut!
EDIT: I made another example, this time with planets of equal sizes, so it's easier to see where the barycenter is (in this case it's the place where the planets are touching each other). This time I also made the very first orbit much more elliptical, so it's completely clear that the barycenter is at one of the focus points of the ellipse right from the start.
Recently I was toying with an old Flash game titled The Orbit Game and I discovered that an elliptical orbit marks a perfectly round donut!
EDIT: I made another example, this time with planets of equal sizes, so it's easier to see where the barycenter is (in this case it's the place where the planets are touching each other). This time I also made the very first orbit much more elliptical, so it's completely clear that the barycenter is at one of the focus points of the ellipse right from the start.
Sunday, 19 April 2026
2026 World Snooker Championship has already started!
(Originally posted on Sunday, 19 April 2026)
2026 World Snooker Championship has already started!
Last year the winner was Zhao Xintong. Congratulations!
This snooker season has been special for fans from Poland because there are three Poles in the Main Tour. MichaĆ Szubarczyk stole the show for some time because he is so young (only 15 years old right now), but in the end it's Antoni Kowalski who is in the spotlight. Right now Kowalski plays in the first round of the 2026 World Snooker Championship (the main tournament) against my favorite snooker player of all time Mark Williams. Kowalski started really good:
This year I would be very happy if the winner were one of these players (ordered according to the tournament ladder):
Ding Junhui
Shaun Murphy
Ronnie O'Sullivan (finally a “mortal” man)
Neil Robertson
Stan Moody
Barry Hawkins
Mark Williams
Antoni Kowalski
Judd Trump
I have to add that I root AGAINST Wu Yize for what he did against Michael Holt (Wu Yize knew the white ball was incorrectly re-spotted and didn't point it out to the referee). By the way: I don't respect anybody who claims that Michael Holt was also to blame because NOBODY, as an opponent to the snookered player, verifies re-spotting balls by the referee, which makes that “rule” completely moot. If Wu Yize apologized specifically for that incident I would change my mind (he is a very talented player, but his sportsmanship is poor).
2026 World Snooker Championship has already started!
Last year the winner was Zhao Xintong. Congratulations!
This snooker season has been special for fans from Poland because there are three Poles in the Main Tour. MichaĆ Szubarczyk stole the show for some time because he is so young (only 15 years old right now), but in the end it's Antoni Kowalski who is in the spotlight. Right now Kowalski plays in the first round of the 2026 World Snooker Championship (the main tournament) against my favorite snooker player of all time Mark Williams. Kowalski started really good:
This year I would be very happy if the winner were one of these players (ordered according to the tournament ladder):
Ding Junhui
Shaun Murphy
Ronnie O'Sullivan (finally a “mortal” man)
Neil Robertson
Stan Moody
Barry Hawkins
Mark Williams
Antoni Kowalski
Judd Trump
I have to add that I root AGAINST Wu Yize for what he did against Michael Holt (Wu Yize knew the white ball was incorrectly re-spotted and didn't point it out to the referee). By the way: I don't respect anybody who claims that Michael Holt was also to blame because NOBODY, as an opponent to the snookered player, verifies re-spotting balls by the referee, which makes that “rule” completely moot. If Wu Yize apologized specifically for that incident I would change my mind (he is a very talented player, but his sportsmanship is poor).
Tuesday, 7 April 2026
Understanding and using Minkowski diagrams (spacetime diagrams)
(Originally posted on Thursday, 26 March 2026; updated on 7 April 2026)
If anybody is interested in Minkowski diagrams (spacetime diagrams), I've made a video on this topic. Enjoy!
If anybody is interested I prepared day-by-day RELATIVISTIC calculations for acceleration of 1G:
Part 1 (from 0:00 to 2:28)
Minkowski diagrams (spacetime diagrams) are rendered with straight lines, so they assume INSTANT acceleration which is simply not possible. I was curious how good an approximation they are, so I prepared day-by-day RELATIVISTIC calculations for acceleration of 1G (acceleration on the surface of Earth due to Earth's gravity).
In my video “Understanding and using Minkowski diagrams (spacetime diagrams)” in the step 9 I described a classic case of twins, where the time on Earth is 8 years, while the time on a spaceship is 6.92 years (ship's time). At that case the ship was moving with the speed of 0.5c, so in my day-by-day calculations I “stopped the acceleration” after reaching the speed of 0.5c. Please notice that I use the notation “v” which means velocity (speed as a vector).
The precise day-by-day result is 7.10 years (ship's time), which is much closer to the result from the Minkowski diagram that I thought it would be.
Part 2 (from 2:29 to 3:22)
By the way I discovered that with acceleration of 1G a spaceship could reach almost the speed of light in around 354 days ship's time. ONLY 354 days ship's time!!! At that moment ANY distance would shrink to almost zero, so the ship could reach ANY place in a universe almost instantly (from the point of view of the ship). From the point of view of Earth the ship would still need millions of years to reach another galaxy, but I think some people would like to take part in such a “one-way journey” (of a spaceship into the future) anyway.
The problem is that the amount of fuel needed to accelerate with 1G for almost a year and then to decelerate with 1G for almost a year would be insane, so the problem is practical (not theoretical).
Part 3 (from 3:23 to 4:24)
At the end of the video I changed the starting speed to 0.5c and the acceleration to ZERO because I wanted to verify my formulas by comparing the result to the Minkowski diagram (spacetime diagram). I ended up with 6.9289 years (ship's time), so the result was the same when rounded down, which means that my formulas were correct. The result had to be rounded DOWN because in the Minkowski diagram (spacetime diagram) I used a rounded value of the Lorentz factor (1.155 instead of 1.1547).
At the speed of 0.5c the relativistic factor (Lorentz factor) is precisely 1.1547, so one simultaneity plane is equal to precisely 1.73205 years (1.1547 * (1 + 0.5)), which gives the precise result 6.9282 for the Minkowski diagram (spacetime diagram). There is still a slight difference (6.9289 vs. 6.9282), but it's because in the day-by-day calculations I used the Lorentz factor from day TWO. When starting with the speed of 0 it gives almost perfect result, but when starting with the speed of 0.5c the difference is already detectable. So, the correction to the day-by-day calculations with instant acceleration to 0.5c would have to be:
(1264.5311 - 1 + 0.8660) / 365 * 2 = 6.9282
PERFECT!
If anybody is interested in Minkowski diagrams (spacetime diagrams), I've made a video on this topic. Enjoy!
If anybody is interested I prepared day-by-day RELATIVISTIC calculations for acceleration of 1G:
Part 1 (from 0:00 to 2:28)
Minkowski diagrams (spacetime diagrams) are rendered with straight lines, so they assume INSTANT acceleration which is simply not possible. I was curious how good an approximation they are, so I prepared day-by-day RELATIVISTIC calculations for acceleration of 1G (acceleration on the surface of Earth due to Earth's gravity).
In my video “Understanding and using Minkowski diagrams (spacetime diagrams)” in the step 9 I described a classic case of twins, where the time on Earth is 8 years, while the time on a spaceship is 6.92 years (ship's time). At that case the ship was moving with the speed of 0.5c, so in my day-by-day calculations I “stopped the acceleration” after reaching the speed of 0.5c. Please notice that I use the notation “v” which means velocity (speed as a vector).
The precise day-by-day result is 7.10 years (ship's time), which is much closer to the result from the Minkowski diagram that I thought it would be.
Part 2 (from 2:29 to 3:22)
By the way I discovered that with acceleration of 1G a spaceship could reach almost the speed of light in around 354 days ship's time. ONLY 354 days ship's time!!! At that moment ANY distance would shrink to almost zero, so the ship could reach ANY place in a universe almost instantly (from the point of view of the ship). From the point of view of Earth the ship would still need millions of years to reach another galaxy, but I think some people would like to take part in such a “one-way journey” (of a spaceship into the future) anyway.
The problem is that the amount of fuel needed to accelerate with 1G for almost a year and then to decelerate with 1G for almost a year would be insane, so the problem is practical (not theoretical).
Part 3 (from 3:23 to 4:24)
At the end of the video I changed the starting speed to 0.5c and the acceleration to ZERO because I wanted to verify my formulas by comparing the result to the Minkowski diagram (spacetime diagram). I ended up with 6.9289 years (ship's time), so the result was the same when rounded down, which means that my formulas were correct. The result had to be rounded DOWN because in the Minkowski diagram (spacetime diagram) I used a rounded value of the Lorentz factor (1.155 instead of 1.1547).
At the speed of 0.5c the relativistic factor (Lorentz factor) is precisely 1.1547, so one simultaneity plane is equal to precisely 1.73205 years (1.1547 * (1 + 0.5)), which gives the precise result 6.9282 for the Minkowski diagram (spacetime diagram). There is still a slight difference (6.9289 vs. 6.9282), but it's because in the day-by-day calculations I used the Lorentz factor from day TWO. When starting with the speed of 0 it gives almost perfect result, but when starting with the speed of 0.5c the difference is already detectable. So, the correction to the day-by-day calculations with instant acceleration to 0.5c would have to be:
(1264.5311 - 1 + 0.8660) / 365 * 2 = 6.9282
PERFECT!
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