I got an SSR (Picker PCS15-D-240A-25ZL) to control a single phase 240VAC North American circuit going to a heating element on a homebrew setup. One of the load wires goes through the SSR and the other goes straight to the output so that the circuit can only be completed when the SSR connection is closed. I tested the heating element plugged directly into the wall circuit and it works fine. Then I moved to testing through the SSR and noticed the heating element wasn't producing any heat. I decided to see what was up with a multi-meter. Checking the output I noticed that difference between the two load wires was approximately zero volts which was odd. Then I decided to check from one post of the SSR to the other when it was closed and noticed a voltage difference of 240v. So is the SSR changing the phase of the power somehow and if so how can I resolve the issue?
Your voltage measurements just confirm that the SSR is not turning on.
Figure 1. With SW1 open VM1 will read full line voltage and VM2 will read zero.
The PCS15-D-240A-25ZL has built-in status LED. This should turn on when you have > 4 V DC on the input. If the LED isn't on then check the input voltage and make sure that it is DC. Note that the LED confirms control voltage and not the output voltage.
If you can't get it going then add a schematic to your question and, perhaps, a photo of your setup.
So is the SSR changing the phase of the power somehow ...?
No. It's just not turning on. I've written a little more on SSRs in Opto-triacs, solid-state relays (SSR), zero-cross and how they work