Ain't gonna happen. The PS4-version would have to run the exact same physics as the PS3-version, and I guess we all would hope they can improve on it with the resources available on the PS4...
I believe that if they did a dual release, they would go ahead and make GT6 PS4 a different game in many ways. It would practically have to be. Very short loading times would just be the start.
The Movie Maker would finally be possible because of the crazy amount of ram and processor power in PS4. Spectating would be routine, and online would be much more powerful. The Course Maker might be like we have in ModNation Racers, a true terrain builder but in HD. The Livery Editor could be much more powerful. Lighting, especially night lighting, would be jaw dropping, and shadows would finally look about perfect. Weather effects and time of day transitions would be impeccable, and precipitation would have a marked impact on grip. Tire modeling and car ballistics could be amazingly lifelike, and we'd finally see a serious damage implementation. Rally racing should be amazing, and a total blast. Race fields could be much more than 24 cars deep, allowing for serious multiclass racing, even online if the network SONY is building is as lag free as they think it will be.
There are a lot of things I'm sure Polyphony would want to do with that PS4 power, and would make GT6 on it a very desirable game. I think fans would throw a fit if they were the same game on both systems, and this reminds me of amar212's post about PS3 getting "finger food, while PS4 will celebrate." And as he said a few days ago, if "nobody will be disappointed," I wonder if SONY would do that dual release after all.
Do better physics demand so much power?
They do, and it depends on what else the game is demanding of the system. In my post of a couple days ago, when I mentioned racing in my other games, the PC sims are pushing very dated visuals on the order of high res PS2 graphics. The bots are mostly polite and pursue their pre-determined race strategy. Damage is barely rendered at all visually, though Live For Speed uses basic crumple cardboard/putty body deformations. So with those two, most of the available resources are going to physics modeling.
In the case of Forza, graphics are about as important as with Gran Turismo. In Forza 4, they did some shortsheeting, much like was done with Toca Race Driver. For instance, in multi-model races, they use generic engine samples except for your car, and this shows up in replays. They used to drop detail in the bot cars a lot, so much so that in Forza 2 they almost looked like inflatable models. It wasn't quite that bad in Gran Turismo games, but they would do things like drop some detail, shadows would vanish, as well as tinted windows, headlights would be off, environment reflections on windows were copied from your car - GT5 still does this, etc. Also, with the bot cars giving up when you get a certain distance ahead of them, that frees up resources to focus on the cars within a certain range of you.
It's like a budget, and there is only so much horsepower to go around. Think of it like money. When you're a kid, and you have $5, and you want to do five things, you could spend a dollar on them evenly. If you really want something special and sweet, you could spend half or more on a pie or tub of ice cream, but that wouldn't leave much for anything else, like the arcade. As you get older, your budget grows with you, and you're spending hundreds to thousands of dollars.
In the case of PS3, you could say it gives you a budget of $500. And with GT5, it seems they spent $200 on graphics and $200 on physics, leaving little for other things like bot A.I. and weather effects, and maybe a dollar or two for damage. But with PS4, your budget is now more like $8,000. If you spent ten times the budget on physics, you still have 75% of those resources available to play with. This is why I'm with people like RandomCarGuy, and anxious to see GT6 on that.