Rav Hai Gaon in תשובות הגאונים החדשות, מהד' עמנואל סי' קטו, עמ' 125 states that there are books which contain the practical kabbalistic methods for achieving k'fitzat hadereh (miraculous speedy travel)
ודבר ברור ומפורסם לאנשי ספרד ומסורת בידם מאבותיהם כי מר נטרונאי גאון ז"ל בקפיצת הדרך בא אליהם מבבל ורבץ תורה וחזר וכי לא הלך בשיירא ולא נראה בדרך. וכמה ספרים מצויין אצלינו כתוב בהם מהשמות וכמה שמות מלאכים וצורת חותמות ואומ' הרוצה לעשות כך והרוצה להגיע לכך יכתוב כך וכך כמו זה על כך וכך ויעשה כך ויתקיים לו המעשה
I would like to know what exactly those instructions are. Meaning the names and symbols which need to be written and in what order etc.
https://youtu.be/IFTNJ2F38Mc - This a video by Rav Meir Eliyahu describing in detail from Rabbeinu Amar the steps needed for this to be done.
Here are the main points:
There are 2 options of doing קפיצת הדרך, One: Enabling a person to travel 1 years worth into a day, two: 1 months worth into 1 hour.
Take a klaf of a deer and write down 10 holy names (that he doesn't mention for obvious reasons).
Write down the pasuk in Vayetzei 28:11, וַיִּפְגַּ֨ע בַּמָּק֜וֹם וַיָּ֤לֶן שָׁם֙ כִּי־בָ֣א הַשֶּׁ֔מֶשׁ וַיִּקַּח֙ מֵאַבְנֵ֣י הַמָּק֔וֹם וַיָּ֖שֶׂם מְרַֽאֲשֹׁתָ֑יו וַיִּשְׁכַּ֖ב בַּמָּק֥וֹם הַהֽוּא׃, and put the 10 holy names around it (all the writing should be done with a קנה- a reed I think, 4 amot tall).
He should role it up, and put it in the reed, and (ירכב עליו, which I'm not sure what he means by this).
Then he should close his eyes and he will be in a different place.
He mentions that this is tried and tested and it works.
I say that answer lies clearly in the talmud Makkos 5a where it discusses a case that עדים testified about an individual that killed someone in the morning in the city of סורא, then other עדים testified against those witnesses that it cannot possible be true because they we're with them that night in נהדרעא, the talmud rules that we calculate the distance between the cities סורא to נהדרעא and if one cant reach there from morning until evening then the עדים are clearly false witnesses and we kill them , the talmud concludes that we dont say that maybe the עדים can get there speedly using a FLYING CAMEL cause it isnt really a possibility. Now if קפיצת הדרך can be done then why would the talmud have those witnesses killed maybe they knew those kaballistic secrets!!! CLEARLY IT CAN NOT BE DONE. see talmud sanhedrin 95 that only 3 merited קפיצת הדרך and they are אליעזר עבד אברהם-יעקב אבינו-אבישי בן צרויה.
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The historian David Solomon has a pretty comprehensive explanation of this topic
in a podcast here
To summarize there are a number of options
Using a special name of Hashem (42 letter, or perhaps 87[?] letter) - the name is uttered and the person is transported. Or in the case of certain righteous people like the Baal Shem Tov, his entire coach is transported.
Using an elaborate ceremony involving a ram's horn (found in the work Brit Menucha) - the horn is made to grow a reed which functions similar to a magic broom, the person mounts the reed and thinks of a destination and is taken there instantly.
Mystical meditation where the soul leaves the body and can then bring the body along
Solomon also mentions that according to the Ari Z'l the reason the first two options work is because there are demons who travel instantaneously and these methods harness demons who are invisibly effecting the transport.