In Canada, copyright means "the sole right to produce or reproduce the work or any substantial part thereof in any material form whatever, to perform the work or any substantial part thereof in public..." (Copyright Act §3(1)).
This question asks whether the work or any substantial part of the work is reproduced when an individual torrent chunk (typically approximately 1/1500th of a file) is downloaded to volatile RAM and immediately discarded.1
If not, is a substantial part of the work reproduced if the downloader-and-discarder repeats the activity on more of the torrent's chunks (each being discarded before downloading another torrent chunk)?
Substantiality
As quoted above from the Copyright Act, when reproducing only a portion of a work, the statute only prohibits reproduction of a "substantial part" of the work.
"[T]he Act does not protect every “particle” of an original work" (Cinar Corporation v. Robinson, 2013 SCC 73).
Substantiality is not measured by quantity. "Whether a part is substantial must be decided by its quality rather than its quantity" (Ladbroke (Football), Ltd. v. William Hill (Football), Ltd., [1964]).
Copyright Board's substantiality decisions
Is a small chunk of a torrent a substantial part?
The Copyright Board has looked to several signals in judging substantiality, one of which is whether "[the part] may be so closely identified to the work as to allow the reader to recognize the work" (License Application by Pointe-à-Callière, Montreal Museum of Archeology and History for the Reproduction of Quotations, Copyright Board of Canada [2004]). In some video codecs, possessing 1/1500th of the encoded file would not allow playback such that the result would be recognizable as a portion of the original.
The Copyright Board has also held that in the case of XM satellite receivers, which hold "4 to 6 seconds of the Satellite Services' multiplex signal at all times in its random access memory (RAM)", that "the 4 to 6 second buffer fails to satisfy the substantiality requirement. It is not a substantial part of the protected work." (Collective Administration of Performing Rights and of
Communication Rights (Re) [2009]).
If downloading and discarding one torrent chunk is not reproduction of a substantial part, does downloading and discarding multiple (even all) chunks become a reproduction of a substantial part of the work?
The Copyright Board has said, regarding the 4-6 second buffer in the XM satellite receiver (ibid.):
"The rolling 4 to 6 seconds of a musical work is not an aggregate of an entire work. At no time does a subscriber possess a series of 4 to 6 second clips which when taken together would constitute a substantial part of the work. It matters not that over time the totality of all works
transmitted are reproduced. We are dealing with a rolling buffer and at no time can we line up all of the fragmented copies amounting to one complete copy of a musical work."
Discussion
In my opinion, downloading a chunk of a torrent file to RAM and immediately discarding it is not reproduction of a work or a substantial part thereof. It is not copyright infringement. Repeating this activity for several torrent chunks of the same torrent file is likewise not copyright infringement.
The above analysis is dependent on assumptions regarding the type of file (a media file, encoded using a format that doesn't produce recognizable sub-portions2, split into approximately 1500 chunks).
Other types of files and torrents would not fall under this analysis and thus the hypothetical download-and-discard activity could still be infringement. Consider a 5 minute .wav file, split into a torrent having only 2 chunks. A 2.5 minute .wav chunk would be recognizable as a portion of the 5 minute original, and 2.5 minutes of a 5 minute work would be much more likely to be considered a substantial part.
Notes
1. I know of no torrent client that behaves this way. It would have to be a custom-written torrent client designed specifically for this ostensibly useless task.
2. Although, I don't think the assumption of unrecognizable subportions is necessary, since the 4-6 second buffer in the XM Satellite receiver was recognizable.