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Tremorsense detects material-based vibrations. Obviously, this refers to sound waves (“tremors”) in the real world. Interestingly, it specifically excludes flying creatures, which could be interpreted to imply that it excludes air-based vibrations.

Wearing the Boots of Elvenkind means the wearer’s footsteps are silent — i.e. produce no vibrations. That could be interpreted to mean sound waves through the air (only), or all sound waves, including those through the ground, which could otherwise have been detected by tremorsense.

Is there any rule or ruling on this interaction?

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    \$\begingroup\$ What's your actual question? It's kind of implied, but not clearly stated. Is it "How does tremorsense interact with someone wearing Boots of Elvenkind?" or more specifically, "Can a creature with tremorsense detect a character wearing Boots of Elvenkind?" \$\endgroup\$ – V2Blast Apr 8 at 4:51
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    \$\begingroup\$ Sent in an edit - if this doesn't match your intent, please, by all means let us know. \$\endgroup\$ – Stackstuck Apr 8 at 8:05
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There is no specific ruling

There doesn't appear to be any specific ruling regarding Boots of Elvenkind and Tremorsense (if there was you would expect it to be mentioned in the description of the boots since this is obviously where any rules specific to how this item interacts with other rules would be).

Hence, by RAW, the boots would make no difference to Tremorsense.

Tremorsense states it enables the creature to pinpoint:

...the origin of vibrations within the specific radius, provided that the monster and the source of the vibrations are in contact with the same ground or substance.

It doesn't actually say about creatures needing to move, and it should be worth noting that the boots only state that your steps make no sound, but presumably any other sounds you make would still be transmitted through your feet to the ground (and you would, potentially, still make sounds which is why the boots only provide advantage on stealth checks to move silently rather than an automatic success).

However

Despite the general danger of trying to apply scientific principles to magical stuff in the world of D&D rules, which hardly ever works, there is enough ambiguity here for the DM to apply some common-sense house-rules if he/she wishes. E.g. Requiring the creature with tremorsense to make a Perception check, with advantage perhaps, rather than automatically pinpointing the location of the sneaky Boots of Elvenkind wearer.

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    \$\begingroup\$ Actually, applying scientific principles works most of the time! :-) We just don't think about it because we take it for granted. It's just when a player or DM is looking for a loophole in the rules — something that would work a certain way in the real world, but probably does not (but might!) work in the gaming system — that is, when we're wanting to not suspend disbelief — that we notice science breaking down. \$\endgroup\$ – jvriesem Apr 8 at 19:36
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No. Boots of Elvenkind produce no sound, but they do produce vibrations

Tremorsense states:

A monster with tremorsense can detect and pinpoint the origin of vibrations within a specific radius, provided that the monster and the source of the vibrations are in contact with the same ground or substance.

It detects vibration through the ground or other materials that both are in contact with.

Boots of Elvenkind states:

While you wear these boots, your steps make no sound, regardless of the surface you are moving across.

While sound is vibrations, to say that all vibrations is sound is incorrect. Sound is only audible vibrations. Tremorsense detects all vibrations.

You can think of tremorsense as a superset of normal hearing. It is a hypersensitivity to vibrations. There is no ambiguity, Boots of Elvenkind of extremely powerful, but not so useful against tremorsense.

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  • \$\begingroup\$ There are lots of vibrations and sounds that are not audible to me. For instance, my dog can hear a dog whistle because her ears can pick up higher frequency vibrations than mine can. My cats hear my wife coming home before I do because their ears are more sensitive than mine (in pitch and volume). In space, something could be vibrating, yet I wouldn't hear it if we were separated by a vacuum — yet it's still producing sound (put an ear or hold a microphone up to it). So I dunno! \$\endgroup\$ – jvriesem Nov 21 at 19:15
  • \$\begingroup\$ @jvriesem What aren't you sure about? I'm sure you can feel an earthquake, but you probably struggle to feel the vibrations of your dog walking around the house! \$\endgroup\$ – jgn Nov 21 at 22:28
  • \$\begingroup\$ Exactly! So, does magic work one way for creatures with good ears and another way for people with less sensitive ears? Does it depend on a cutoff frequency or volume? I doubt it. \$\endgroup\$ – jvriesem Nov 21 at 22:36
  • \$\begingroup\$ @jvriesem The boots make no sound. However you should note that non-audible vibrations are not "sound". Tremorsense detects these non-sound vibrations through solid surfaces. Even if the vibrations are outside the hearing range of all creatures in existence, a creature with tremorsense could detect them. It is these vibrations which the boots do not muffle which are the problem. \$\endgroup\$ – jgn Nov 21 at 22:59

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