Okay, so wizards have Floating Disk available to them at 1st level, and when you cast it as a ritual it won't expend a spell slot. Then, you could use Silent Image to make the disks appear to be chairs, tables, and other solid surfaces. It's like having a portable living room wherever you go! 

Next, if you cast Floating Disk, and attach a 25-foot plank to it (probably with an Arcane Locked rope or chain), then attach yourself to the other end of the plank by blocking the disk, and using the same method. After you do this, the disk will try to catch up to you, but will be unable to because you are always 25 feet away. This keeps going until you reach about 0.6c, (relative to the observer)  at which point the length contraction would have caused the plank to become 20 feet and caused the disk to stop. Basically, the disk will accelerate, stop, and repeat. The time dilation at this point would be somewhat significant, one hour (the spell's duration) in your frame would be about 1.04 to 1.25 hours to everyone else. Also traveling at this speed with no protection would probably kill you.

Just so you know, I am not one of the people who tries to break the game. I just like an opportunity for some interesting math in a fantasy setting.

Please tell me if I got anything wrong.

Quote from WizardlyHedgehog >>

Okay, so wizards have Floating Disk available to them at 1st level, and when you cast it as a ritual it won't expend a spell slot. Then, you could use Silent Image to make the disks appear to be chairs, tables, and other solid surfaces.

 Silent image create an image of an object out of thin air, it doesn't modify the appareance of an existing one.

Firstly I can't see anywhere in the spell that describes the acceleration of the disk or the force it applies if it can't keep up.

Secondly if it did have the potential to accelerate without limit the disk and passenger wouldn't be in the same frame of reference so there'd be no Lorentz contraction - the disk would stay 25' away from the observer in their frame of reference and you'd end up accelerating forever. 

Thirdly the default D&D would has loads of problems with physics at the best of time so trying to apply even Newtonian mechanics to it is probably an exercise in futility before even thinking about bringing Einstein into the fold.

 Edit: Replaced wouldn't with would. Bugger.

Quote from WizardlyHedgehog >>

Basically, the disk will accelerate

Why?

Quote from WizardlyHedgehog >>

Next, if you cast Floating Disk, and attach a 25-foot plank to it (probably with an Arcane Locked rope or chain), then attach yourself to the other end of the plank by blocking the disk, and using the same method. After you do this, the disk will try to catch up to you, but will be unable to because you are always 25 feet away. This keeps going until you reach about 0.6c, (relative to the observer)  at which point the length contraction would have caused the plank to become 20 feet and caused the disk to stop. Basically, the disk will accelerate, stop, and repeat. The time dilation at this point would be somewhat significant, one hour (the spell's duration) in your frame would be about 1.04 to 1.25 hours to everyone else. Also traveling at this speed with no protection would probably kill you.

 I appreciate the thought experiment.

Floating Disk is of course just a plane of force. You cannot attach something to it. Arcane Lock does not let you attach things to planes of force. Once the forward acceleration of the disc is greater than the force of gravity, anything on the disc would simply "fall" backwards off the disc.

In game, as a DM, I would just rule that the disc has a "speed limit" to try to catch up to you, probably no faster than your dash movement speed. But still funny to imagine you "driving" your disc to the next town.

Quote from Aescleal >>

Firstly I can't see anywhere in the spell that describes the acceleration of the disk or the force it applies if it can't keep up.

Secondly if it did have the potential to accelerate without limit the disk and passenger wouldn't be in the same frame of reference so there'd be no Lorentz contraction - the disk would stay 25' away from the observer in their frame of reference and you'd end up accelerating forever. 

Thirdly the default D&D would has loads of problems with physics at the best of time so trying to apply even Newtonian mechanics to it is probably an exercise in futility before even thinking about bringing Einstein into the fold.

 

 Yeah. You make a good point. I'm still new to physics, so I still make a lot of mistakes.

I thought it would accelerate because you would be farther than 20 feet away from it and the spell states that "The disk is immobile while you are within 20 feet of it. If you move more than 20 feet away from it, the disk follows you so that it remains within 20 feet of you" and the pole isn't really an obstacle, it just keeps you farther away for a while so the disk tries to catch up.

The disk only moves when you move away from it.  that movement is simultaneous, at the exact same speed you move.  You can never get to the end of the 25 ft plank.  I.e. it does not wait for you to move from 20 ft to 25 ft, it moves to 20 ft when you try to move to 20.000001 ft.

Quote from Plaguescarred >>

Quote from WizardlyHedgehog >>

Okay, so wizards have Floating Disk available to them at 1st level, and when you cast it as a ritual it won't expend a spell slot. Then, you could use Silent Image to make the disks appear to be chairs, tables, and other solid surfaces.

 Silent image create an image of an object out of thin air, it doesn't modify the appareance of an existing one.

 I was thinking that, now that you have pointed out that error, that image is just there, it doesn't modify any appearances. The disks are just there to make a place to sit, so don't try to lean back in the chairs. You can see the disks.

Quote from Mog_Dracov >>

The disk only moves when you move away from it.  that movement is simultaneous, at the exact same speed you move.  You can never get to the end of the 25 ft plank.  I.e. it does not wait for you to move from 20 ft to 25 ft, it moves to 20 ft when you try to move to 20.000001 ft.

 

Ah. This plan has quite a lot of errors. I  thought maybe the party's barbarian holds the wizard out on a 25 foot pole from the disk, and I was thinking that an arcane locked thing would make it more sturdy. 

Quote from PeteInCary >>

Quote from WizardlyHedgehog >>

Next, if you cast Floating Disk, and attach a 25-foot plank to it (probably with an Arcane Locked rope or chain), then attach yourself to the other end of the plank by blocking the disk, and using the same method. After you do this, the disk will try to catch up to you, but will be unable to because you are always 25 feet away. This keeps going until you reach about 0.6c, (relative to the observer)  at which point the length contraction would have caused the plank to become 20 feet and caused the disk to stop. Basically, the disk will accelerate, stop, and repeat. The time dilation at this point would be somewhat significant, one hour (the spell's duration) in your frame would be about 1.04 to 1.25 hours to everyone else. Also traveling at this speed with no protection would probably kill you.

 I appreciate the thought experiment.

Floating Disk is of course just a plane of force. You cannot attach something to it. Arcane Lock does not let you attach things to planes of force. Once the forward acceleration of the disc is greater than the force of gravity, anything on the disc would simply "fall" backwards off the disc.

In game, as a DM, I would just rule that the disc has a "speed limit" to try to catch up to you, probably no faster than your dash movement speed. But still funny to imagine you "driving" your disc to the next town.

 Yeah, a speed limit is a good idea. 

Evidently, this floating disk thing has plenty of flaws which have been pointed out. Thank you everyone for helping me figure out all the errors in this plan! :)

Thank you for clearing this up

Quote from Mog_Dracov >>

The disk only moves when you move away from it.  that movement is simultaneous, at the exact same speed you move.  You can never get to the end of the 25 ft plank.  I.e. it does not wait for you to move from 20 ft to 25 ft, it moves to 20 ft when you try to move to 20.000001 ft.

 

 You could use Misty Step to move to the end of the board.

If you were on that board at 25 feet from the disk, I would rule that the disk would not move, because it will not move if it cannot move closer. It would not satisfy the idea of "following you" if you were moving with it.

If you were to cast Dimension Door to a space exactly 99 feet away, the disk would then start moving towards you. I would still have the disk move at a certain speed and not have it instantly catch up to covering that distance in an instant.

The teleport issue is interesting.

I personally would solve the issue by having the disk teleport with you.  It is a magical spell cast on you, so just as I would have a fly spell stay on you when you teleport, so would the disk.

Then the question becomes what happens to things on the Disk when it teleports with you.   I would allow you to take them with you for a misty step, but for dim door it has a weight limit, so I would enforce the weight limit.  Might end up leaving stuff behind...

Quote from PeteInCary >>

If you were on that board at 25 feet from the disk, I would rule that the disk would not move, because it will not move if it cannot move closer. It would not satisfy the idea of "following you" if you were moving with it.

See, but then that takes away the ridiculousness of having someone build a disk-powered "car" more than 20 feet long, where the wizard sits up at the very front and the disk is cast at the rear.