I was recently learning about pressure in my high school science class. I will admit that I am not extremely well educated in the subject and thus this may be an extremely stupid question. But anyways, I was curious about if in any way one could possibly make a forcefield or at least something that could repel objects coming towards you. My idea was that if you were able to create enough pressure (via heat), so much so that it was being made even faster than it was being released, that you could repel objects. Because of the objects having a lower amount of pressure than your "forcefield" the high pressure would, in theory, go towards the low pressure and push the object away. Again this may be a very stupid question but I was curious about whether our not it could work.
A localised area of high pressure 'pushes' against the incoming object due to the air flowing from high pressure to low pressure.
I imagine you'd need an unrealistically high windspeed to push away anything that needs to be repelled. Especially if you're thinking of something like bullets which are shaped to be as aerodynamic as possible anyway.
To clear up your thinking about this, you may want to consider pressure as a force (technically it's a force distributed over an area, but that's not too important just yet), not as a thing which has a physical form. When you wave your hand through the air, you're creating an area of high pressure in front of your hand by pushing air molecules around.
Likewise, if you radiate a lot of heat into the air you will create an area of high pressure by increasing the kinetic energy of the air molecules. Since there's no container around your energy source, the air molecules will stream down the pressure gradient into the surrounding atmosphere. We usually call this phenomenon wind. Indeed, this is the same basic mechanism that creates large-scale winds on earth (the sun is the heat source).
If you want to stop something like a bullet with a pressure wave (read: blast of wind), you need to eat up all of its energy, which mean decelerating it. A pressure wave in air is going to be about 200nm thick(1), a rifle bullet travels around 730m/s(2), a mass of about 8g(2), and a has a profile of about 50mm^2(2)†. A quick calculation shows us that we need a pressure wave of about 200*10^12 Pa, or about 200TPa.
That's a lot. For reference, that's closing in on the pressure inside an exploding nuclear bomb(3). So, while it's theoretically possible to stop a bullet with a pressure wave, you wouldn't exactly doing the user any favors; whoever tries to use this air pressure shield is going to end up very dead.
You might do OK against arrows though.
†Bullets are streamlines, so it's not quite right to treat it like a disc with a 4mm radius flying though the air, but since this pressure wave is so extreme I think it's a fine approximation.
I think it works, but not at the scale you want.
So, I'm pretty sure I've seen something similar in real life - using pressure, heat and movement to repel objects without touching them. It's just, the scale is so tiny it would never work for bullets.
Soooo... have you ever noticed, when driving, when snowing, with the windshield heat on full blast, at a certain speed, the snowflakes very abruptly stop hitting the windshield, and just flow over and around the edges, no wipers needed? But all the qualifiers are necessary, because if you're not driving fast enough, the windshield isn't hot enough, and if it isn't snowflakes but rain, slush, sleet, or anything else, it hits the windshield, melts, and obstructs your vision.
(possibly I think too much. or notice too much. ah, well)
Anyway, we have a sharp difference in heat, and because of that a difference in pressure. We have a good clip of windspeed from the car moving against the air. The difference is just enough for the snowflakes to be repelled by the difference in pressure and temp, and slide around the "force-field" (helped by wind-speed) instead of smacking against the windshield. Theory is looking good, as per c.z.'s answer.
On the other hand, the windspeed is a lot - you're going pretty fast, faster than you would want the wind to hit you at without a car in the way (why windows should stay shut at highway speeds). And the difference in heat from the full front heater to the glass (which holds the heat close and provides radiant surface) to the snowy air is a fair amount - workable, yes, but noticable. And that pressure is only just enough to lift snowflakes.
Enough heat to create the same pressure difference without the added wind-speed from high speed motion, or even without the glass barrier concentrating the heat as a surface instead of gradient would be...more. Add in the amount you would need to increase the whole effect to deflect anything bigger than snowflakes, and I'm guessing it varies between "not possible" and "maybe possible, but not useful since those conditions would kill whatever is being shielded".
So next time you're driving in a snowfall, turn your windshield heater on full and notice your force-field at work. Just don't expect it to stop anything bigger :)