As a general rule of thumb crying indicates some kind of discomfort (obviously). As another rule of thumb it's better to let pain (if you can't find out why it's there and how to remove the root cause, which you should always try to do) circulate as opposed to trying to suppress it or distract the child, because pain that is there has to discharge to be really gone and solved. In that respect it's helpful to allow your child to cry.
However it's one of the best-proven facts in child psychology that the way parents respond to a baby's discomfort has a very (really very) strong influence on the rest of the babies' lives, and up to now there's no promising or even scientifically proven way to change the "programming" that parents or other people haven given a person in early childhood in that respect. It's really stable throughout life. If interested in details, read here: https://en.wikipedia.org/wiki/Attachment_theory
For its many positive effects it will have on her whole life it should be the goal that your baby becomes securely attached (as described in the article).
For that I strongly advise not to let her cry alone. At the age of just four months they still do need physical contact to develop properly, especially in times of pain. Everything else will eventually lead to one of the other attachment styles.
I do understand the constraints of today's working life, and if both of you HAVE to work, it's probably also essential for the baby's well-being that you do, and the fact that you're facing these circumstances and dealing with them deserves everyone's respect. Every judgement is inappropriate.
What I do want to point out though is that if you want your baby to "function" the way you want to function in your professional life, it's probably not serving her best.
There are usually two competing aspects in integrating a child into society and it requires a lot of intuition and skill to balance them properly (you too will learn this by doing): On the one hand we've all (including your baby) got primitive nervous systems that simply get conditioned by various stimuli, and in that respect if you don't want your baby to cry, it's better not to encourage it by rewarding it with a lot of attention as she cries and leaving her alone if she doesn't cry.
On the other hand being close to a parent, being carried and held and stroked when in pain, helping her to discharge the pain quickly by feeling with her and offering heartfelt empathy, is just essential for her healthy development. The weight of this fact decreases over time (as kids get older), thus automatically putting more emphasis on the conditioning aspect just mentioned, but at just four months of age, based on what's scientifically proven I definitely would put full focus on the attachment aspect (up to at the very least six months, better at least to one year).
I understand it's inconvenient for you and maybe even worse, but these are the facts I can share with you at this point and with the knowledge I have about your situation.
I also want to assure you that a securely attached child is usually a whole lot easier to handle as they grow up, really in many cases the difference is like two different worlds. Do not undervalue this, especially if you really have to put a strong focus on your everyday comfort and your ability to go to work relaxed every day.
My observation has always been that kids have a strong tendency to sleep in the same bed as their parents until up to at least four years of age if they're not forcefully conditioned to behave otherwise. From the age of four a securely attached child will decrease this behavior on their own if they have an own bed, or at least you can start encouraging them. Every kid is unique though, these are just guiding values which can greatly vary.
As a starting point we should always trust the kid to know what's best for their emotional development.
Four years may sound like an eternity if you're longing for your freedom as the person you were before parenthood. There may also be a couple of cases where it's counterproductive to let a kid do this for that long. And of course the benefit of sleeping in the bed of the parents strongly depends on how comfortable they are with the situation too. But as a general indication I will want to point out this:
If you see a crying baby, you observe him/her for a while, you should realize that they have no way to control this. They're not doing this to upset you or make your life harder, they just need help and love in that very moment. The frequency at which babies ask for this can be horribly tiring, but this still doesn't justify refusing it altogether or based on a schedule.
Again, there are no strict rules that apply to every situation. If you try to find them anywhere, you can read dozens of books with all sorts of contradicting advice. My reply probably is just another one in that line.
You can't actually believe anyone without experimenting what works for you.
The most important bit of advice I can thus give is: Trust your intuition. It's the most precious gift you have, and I'm sure you have it.
Do not allow any book or scientific result or forum post to obscure this intuition, it's really important to nourish and listen to it.
But, and maybe that's the main point I'm try to make: Neither allow the requirements of your jobs to obscure your intuition. The danger is there. Be aware of it, and listen into your heart when your baby is crying what would be the best thing to do for her.
I'm saying this with no strings attached, I'm really not implying anything I'm believing your heart is saying in any given situation. It could be anything, and the only way to know is listening to it.
If you're still unsure about what to do or what the crying means or how to deal with your situation in general, seek advice from a professional (e.g. a child psychologist) near you. These issues can be really complex and a lot of things play a role, even the design of the room or family issues somewhere around you. Of course advice gets better the more the person giving advice knows about you and the baby (including knowing you in person). Out of the box everything can be true or correct as soon as we're talking about a specific situation you're describing, it really depends on the circumstances.
All the best.
